There are 50 and pen and pencil. Each pen cost $6 and each pencil cost $5. The total cost of pens is $47 MORE THAN the total cost of the pencil. How many pen and how many pencil are there?


Pens : 1u
Pencil : 1p

Total cost of pens : 1u x $6 = $(6u)
Total cost of pencils : 1p x $5 = $(5p)

Given
1u + 1p = 50 …………… (1)
$(6u) – $(5p) = $47
6u – 5p = 47 …………….(2)
5u + 5p = 250 …………(3) = (1) x 5
11u = 297 …….[(2) + (3)]
1u = 27 (No. of pens)
1p = 50-27 = 23 (No. of pencils)

Hi Dharma,

I like you solution to this question! Its elegant!
Thanks for teaching me!

Tanks X and Y are each filled with some water. If water from Tank Y is poured into Tank X until the water in Tank X reaches the brim, there will be 8 litres of water left in Tank Y. If water from Tank X is poured into Tank Y until the water in Tank Y reaches the brim, there will be 26 litres of water left in Tank X. The ratio of the volume of Tank X to the volume of Tank Y is 5:3. How many more litres of water are needed to fill both tanks to their brim?



Scenario 1

…Tank X…Tank Y
Before…5 u - A…8 l + A\t\t\t\t
\t\t
…+ A…- A
\t\t
…

After…5 units…8 l
…



Scenario 2

…Tank X…Tank Y
Before…\t26 l + B…\t3 u - B
\t\t
…- B…+ B
\t\t
…

After…26 l…3 units
…


5 u – A = 26 l + B
5 u – 26 l = A + B


8 l + A = 3 u – B
A + B = 3 u – 8 l

5 u – 26 l = 3 u – 8 l
5 u – 3 u = 26 l – 8 l
2 u = 18 l
1 u = 9 l


Ans. A + B = 3 x 9 l – 8 l = 19 l

Tanks X and Y are each filled with some water. If water from Tank Y is poured into Tank X until the water in Tank X reaches the brim, there will be 8 litres of water left in Tank Y. If water from Tank X is poured into Tank Y until the water in Tank Y reaches the brim, there will be 26 litres of water left in Tank X. The ratio of the volume of Tank X to the volume of Tank Y is 5:3. How many more litres of water are needed to fill both tanks to their brim?



Scenario 1

…Tank X…Tank Y
Before…5 u - A…8 l + A\t\t\t\t
\t\t
…+ A…- A
\t\t
…

After…5 units…8 l
…



Scenario 2

…Tank X…Tank Y
Before…\t26 l + B…\t3 u - B
\t\t
…- B…+ B
\t\t
…

After…26 l…3 units
…


5 u – A = 26 l + B
5 u – 26 l = A + B


8 l + A = 3 u – B
A + B = 3 u – 8 l

5 u – 26 l = 3 u – 8 l
5 u – 3 u = 26 l – 8 l
2 u = 18 l
1 u = 9 l


Ans. A + B = 3 x 9 l – 8 l = 19 l

A group of people met a party. Each person shook hands with everyone else. Mr Li shook hands with 3 times as many men as women. Mrs Li shook hands 4 times as many men as women. How many men and how many women were there at the party?



…Men…Women
Clue 1…1+3 units…1 unit
Clue 2… 4 parts…1+1 part

1 unit = 1+1 part;
3 units = 3+3 parts

1+3 units = 4 parts
1+3+3 parts = 4 parts
1 part = 1+3 = 4

Ans.
Men = 4 parts = 4 x 4 = 16
Women = 1+1 part = 1 + 4 = 5

1. Lena and Salimah shared some beads. If Lena gives Salimah 1/2 of her beads, Salimah will have 95 more beads than Lena. If Lena gives Salimah 1/6 of her beads, she will have 15 beads fewer than Salimah.

a. How many beads do the two girls have altogether?
b. If both girls combined their beads and packed them into bags of beads, how many complete bags of 25 beads would they have?

Scenario 1
…Lena…Salimah
Before…12 units…95
…-6 units…+6 units
…
After…6 units…6 units+95
…

Scenario 2
…Lena…Salimah
Before…12 units…95
…-2 units…+2 units
…
After…10 units…2 units+95
…

10 units = 2 units + 95 - 15
10 units = 2 units + 80
8 units = 80
1 unit = 10

Ans.
(a) 12 x 10 + 95 = 215
(b) 215 / 25 = 8 bags



2. There were 310 adults in a hall. When 25% of the men left the hall, and 40 women came in. There was equal number of men and women. How many women were there at first?


…Men…Women
Before…4 units…3 units - 40
…-1 unit…+40
…
After…3 units…3 units
…

4 units + 3 units - 40 = 310
7 units - 40 = 310
7 units = 40 + 310 = 350
1 unit = 50

Ans. At first, women = 3 x 50 - 40 = 110



3. Samuel gets $5 more pocket money than Barbara each week. They each spend $15 per week and save the rest. When Samuel saves $80, Barbara only saves $40. How much pocket money does Samuel get each week?

Total difference = $80-$40 = $40
Individual diff = $5
No. of weeks = 40/5 = 8 weeks

Samuels takes 8 weeks to save $80. He saves $10 each week.

…Samuel
Spending…$15
Savings…$10
…
Pocket Money…$25
…



4. On a farm, there are 1/5 as many hens as goats and twice as many cows as hens. If the total number of legs of the three kinds of animals is 600. How many cows are there on the farm?

…Hens…Goats…Cows
No. of animals…1 unit…:…5 units…:…2 units
…x 2 legs…x 4 legs…x 4 legs
…
Total legs…2 units…20 units…8 units
…

2 units+20 units+ 8 units = 30 units = 600
…1 unit = 20

Ans. No. of cows = 2 x 20 = 40

This is the "After" situation:


Tank —> 12 units
Pail -----> 1 unit

Since the total volume of water remain constant,

13 units = 8346 ml
1 unit = 8346 / 13 = 642 ml

Pail = 1 unit = 642 ml

Ans. At first, Pail = 642 + 314 = 956 ml