tianzhu:

mathnoobs:

Good morning Tianzhu
thank you for replying to my questions early in the morning. Wishing you a good day ahead.

actually both questions have the word left, that's what really got me confused:

Don spent $268 of his savings on a camera and 3/8 of the remainder on a pair of shoes. Then, he bought a bag for $62 and had 1/4 of his savings left. How much savings did Don have at first?

Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the amount of money she had left. Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings left. Finally she had $6219.85 in the bank.
A) how much money did she give to her parents ?
B) how much was her original saving in the bank ?

Hi

In the first question, all the expenses are deducted from the initial or original savings.

Imagine Don were shopping in Takashimaya; he started with an initial amount (612).He paid 268 for a camera. He spent $129 on a pair of shoes and $62 on a bag. After his shopping, he sat down in the food court and counted his remaining money which amounted to 1/4 of the original savings.

In the second question, we have a sequence of events from Jan to March.

In March, she managed to save 40% of her savings left.

This refers to 40% of her savings in March.

Best wishes

Hi Tianzhu
thank you again for answering my queries. Sorry for being so tiresome. It's just that if I don't clarify this, in future, if I see the same type of question, I would not know how to interpret these type of questions, let alone solve it.
If there was some clue on how to interpret this (as you can see, the interpretation \"of his/her savings left\" is different in the 2 questions), it would be very helpful.

In the Don question, it can also be broken down into a sequence of events, just like the Nicole question. In fact, that was how I interpreted it.
The camera purchase was one event, the shoes purchase was another event followed by the bag, a third event.

In the shoe purchase, Don spent \"3/8 of the remainder on a pair of shoes\". The purchase was 3/8 of the remainder, it was not linked to the original savings. After that, that problem said \"then he bought a bag for $62\", which I interpreted it to mean subsequently, since the word \"then\" is there, I interpreted that he paid the $62 out of the remainder and had 1/4 of the remainder left.
Now, normally I would not have interpreted it this way, ie. 1/4 of the remainder, because it said \"1/4 of the savings left\". I would interpret the savings to mean the orignal savings.

However, because of the Nicole question, which also said the same thing \".... of the savings left\", and that was interpreted as the savings left in March, I thought that the Don question should also be interpreted in the same way, afterall they shared the same keywords, and the Don question said \"3/8 of the remainder\" which does constitute a sperate event.

tianzhu:

mathnoobs:

Hi Tianzhu,

this question threw me off, I thought I had understood this type of questions:

Don spent $268 of his savings on a camera and 3/8 of the remainder on a pair of shoes. Then, he bought a bag for $62 and had 1/4 of his savings left. How much savings did Don have at first?

over here, the 1/4 of his savings refers to the original savings Don had, before he spent any money.

however in this question,
Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the amount of money she had left. Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings left. Finally she had $6219.85 in the bank.
A) how much money did she give to her parents ?
B) how much was her original saving in the bank ?

the 40% of her savings refers, not to the original savings Nicole had at the start, but the savings in March.

Both the Don question and the Nicole question uses the keywords, of his/her savings. In the Don question, the savings (1/4) referred to the savings at the start, while in the Nicole question, the savings (40%) referred to the savings in March, not at the start. Shouldn't both questions refer to savings at the start ? so that the interpretation is consistent ?
Or if one follows the Nicole example, then Don's question should have the 1/4 savings refer to the savings after the shoes were bought, not at the start.

Hi mathnoobs

Good Morning.

I think you've missed out the word left in the second question.

Best wishes

Good morning Tianzhu
thank you for replying to my questions early in the morning. Wishing you a good day ahead.

actually both questions have the word left, that's what really got me confused:

Don spent $268 of his savings on a camera and 3/8 of the remainder on a pair of shoes. Then, he bought a bag for $62 and had 1/4 of his savings left. How much savings did Don have at first?

Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the amount of money she had left. Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings left. Finally she had $6219.85 in the bank.
A) how much money did she give to her parents ?
B) how much was her original saving in the bank ?

Hi Tianzhu,

this question threw me off, I thought I had understood this type of questions:

Don spent $268 of his savings on a camera and 3/8 of the remainder on a pair of shoes. Then, he bought a bag for $62 and had 1/4 of his savings left. How much savings did Don have at first?

over here, the 1/4 of his savings refers to the original savings Don had, before he spent any money.

however in this question,
Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the amount of money she had left. Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings left. Finally she had $6219.85 in the bank.
A) how much money did she give to her parents ?
B) how much was her original saving in the bank ?

the 40% of her savings refers, not to the original savings Nicole had at the start, but the savings in March.

Both the Don question and the Nicole question uses the keywords, of his/her savings. In the Don question, the savings (1/4) referred to the savings at the start, while in the Nicole question, the savings (40%) referred to the savings in March, not at the start. Shouldn't both questions refer to savings at the start ? so that the interpretation is consistent ?
Or if one follows the Nicole example, then Don's question should have the 1/4 savings refer to the savings after the shoes were bought, not at the start.

tianzhu:

mathnoobs:

sorry if I'm a bit long winded. But \"In February, she managed to save 1/5 of the amount of money she had left.\", why can't we interpret that to mean say, out of $1,000 in the bank, she saved 1/5 or $200? How would one phrase \"Out of $1,000 in the bank, Peter saved $200 in Feb ?\" , ie. no injection of funds into bank account.

Hi

In February, she managed to save 1/5 of the amount of money she had left.

Precisely, it means out of 1000 in the bank, she saved 200.

In this case, the 1000 is already in the bank account; Nicole went to the bank and top up her account with another 200 (fresh fund).

If there is no injection of fresh fund, where does the 200 come from?

Best wishes

I've finally seen the light...
I interpreted it to mean that out of 1000 dollars in the bank account, after one month, only $200 was left. This would happen if let's say a child's bank account, where the money is spent every month, and there is no money coming in. It's still considered 1/5 is left in the account at the end of the month. I guess it comes down to the interpretation of the word \"saved\". I interpreted it to mean what was left in the bank account. In actual fact, it is interpreted to mean a fresh injection of funds.

heh, you have to understand, we non maths folks interpret things differently from the Maths gurus. that's why we're in the dark when it comes to this type of problems because we don't read it the way it was meant to be read.

anyway, Tianzhu, thank you very much for taking the time to clear out my cobwebs from my brain. Now I know what \"saved\" means in Maths.

mathnoobs:

I realized where my mistake in interpretation was. I interpret \"In February, she managed to save 1/5 of the amount of money she had left.\" as out of the 5 parts that she had left from Jan's savings, she spent some money, and what's left is 1 part. I did not see that as a fresh injection of funds into her account. Rather, I saw it that from her initial savings, the amount kept dwindling every month.

sorry if I'm a bit long winded. But \"In February, she managed to save 1/5 of the amount of money she had left.\", why can't we interpret that to mean say, out of $1,000 in the bank, she saved 1/5 or $200? How would one phrase \"Out of $1,000 in the bank, Peter saved $200 in Feb ?\" , ie. no injection of funds into bank account.

a big thank you to Tianzhu for your very detailed explanation.

After going through the solution very carefully, I finally understood the whole long sequence, and I really mean the sequence. A lot of information are linked sequentially. I realised what \"then\" meant. It didn't mean the next month, it meant the remaining amount for Feb, and then she spent the money on pens, and then she spent the money on her parents. Each new expenditure is based on the amount remaining from the previous expenditure.

All those \"... amount of money she had left\" did not refer to the amount of money saved in Feb, but the subsequent amount after each expenditure.

This is one of the most convoluted question I've ever encountered in Primary school maths. I don't think primary school children can decipher it's meaning under exam conditions. Not because it is difficult but rather, it is so vaguely phrased. If the question had phrase it \".. the amount of money left after buying the pens\" or \"... the amount of money left after saving 1/5 of ...\", it would have been a lot clearer.

Sigh..... can't they just test our children on maths in a Maths exam rather than English comprehension ?

tianzhu:

mathnoobs:

I'm at a loss on the interpretation here:

Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the amount of money she had left. Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings left. Finally she had $6219.85 in the bank.

In Feb, she managed to save ...Then she purchase 8 pens...

The word \"Then\" came after the statement that she saved 1/5 in Feb. That would indicate that she purchased the 8 pens after Feb, therefore in the month of March. She also gave 3/8 to her parents.
The parent statement came directly after the pen statement, so this would indicate that both are on the same time frame, ie. March.

Hi mathnoobs

Speedmaths's answer of 8500 is correct.

To avoid confusion, I'll remove my original post.

The amount of money she saved later is from new sources, maybe from her salary, and added to the amount she had left in her bank account.

Best wishes

I'm afraid I still don't see how the money she spent on pens and the parents came to be under Feb expenses. I would have thought that it belonged to the March expenses, because of the keyword \"then\" , which the problem sum uses to describe the Pen's expenses. If I substitute the word \"after that\" for \"then\" in the problem sum, I would have interpreted the Pens expenses to come in March.

Maybe speedmaths can give his insights as well.
This is all so frustrating. I haven't gotten to solving the problem yet, still figuring out the interpretation of the problem.

I'm at a loss on the interpretation here:

Nicole had saved a certain amount of money. In January, she spent 30% of her savings. In February, she managed to save 1/5 of the amount of money she had left. Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of the amount she had left. In March, she managed to save 40% of her savings left. Finally she had $6219.85 in the bank.

In Feb, she managed to save ...Then she purchase 8 pens...

The word \"Then\" came after the statement that she saved 1/5 in Feb. That would indicate that she purchased the 8 pens after Feb, therefore in the month of March. She also gave 3/8 to her parents.
The parent statement came directly after the pen statement, so this would indicate that both are on the same time frame, ie. March.

tianzhu:

Hi small


Good Morning.

Where is this question from?

Jan
Spent ----- 3 units (15 units)
Remaining ------ 7 units (35 units)

Feb
Saved ----- 7 units (1/5*35units)

8*3.95 ------ 31.6

3 parts ----- parents’ tour

5 parts remaining

2 parts ------saved ------- 6219.85
3 parts ------ 6219.85*3/2 ------ 9329.75 ( money given to parents)
8 parts ------ 24879.40

7 units ------ 24879.4+31.6
7 units ------ 24911
50 units ------ 177935.71 (money in the bank at first)

Best wishes

Hi Tianzhu
this is a really hard question to understand. Thanks for the solution.
However, I am confused by these sentences:

Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of he amount she had left.

It looks like she spent the money in March. So the total amount of money spent in March is (8x3.95) + 3 parts. However, from your workings, it looks like she only spent 3 parts in March. :? I can't see how that is done.

MathIzzzFun:

Chan09:

I do need help as I can solve using algebra but even looking at models this is tough:

a group of friends play tennis. each of them play with everyone else. Ann played with 4 times as many girls as boys. Bob played with 5 times as many girls as boys.
a) how many people were there altogether? ans: 31 people
b) were there more boys than girls and how many more? ans: 19 more girls than boys

Hi

Ann played with 4 times as many girls as boys, so
Girls : Boys --> 4u +1 : 1u,
total 5u + 1 people and there were 3u + 1 more girls

Bob played with 5 times as many girls as boys,
Girls : Boys --> 4u + 1 : 1u -1 = 5 : 1

cross multiply or equalize --> 4u + 1 = 5u -5
1u --> 6
5u + 1 = 31
3u+1 --> 19

There were 31 people and there were 19 more girls than boys.

cheers.

I'm afraid I don't get this:

Bob played with 5 times as many girls as boys,
Girls : Boys --> 4u + 1 : 1u -1 = 5 : 1

why is Boys = 1u-1 ? and Girls = 4u+1 ? is that from the previous statement ?