Q&A - PSLE Math

[MathIzzzFun]

charsen:

How to solve this question ?

The sum of 4 numbers is 80.If you add 3 to the first number, subtract 3 from the second number,multiply the third number by 3 d divide the fourth number by 3,the result will be equal.What is the difference between the largest and the smallest of the original numbers.

hi

Hi
after multiplying 3rd number by 3 --> 3u

1st number --> 3u-3
2nd number --> 3u +3
3rd number --> 1u
4th number --> 9u
Total --> 16u = 80
1u --> 5

1st number --> 12
2nd number --> 18
3rd number --> 5
4th number --> 45

cheers.

[MathIzzzFun]

dicoyote:

Hi MathIzzzFun,

Thank you so much, am amazed at the details you have provided, not only that, even applying side by side with the \"chicken & cow\" logic, which make understanding more easier

Just to clarify my understanding, the \"x3\" uses across for the value is to find a similarity basis for the equation, am I correct? :scratchhead:

Hi

In a \"normal\" chicken-cow type of question, we will have
1 cow --> 4 legs
1 chicken --> 2 legs, OR
1 pen --> $4
1 pencil --> $2

For this question, we have:
Amount collected for 2 vases delivered on time --> $15
Amount collected for 3 vases delivered late --> $10

A straightforward way is to find the unit value :
Amount collected for 1 vase delivered on time --> $ 7.50
Amount collected for 1 vase delivered late --> $10/3 -- not a whole number, and not a \"nice\" fraction like 1/2.
difference --> $7.50 - $10/3 = $ 25/6 -- amount collected less due to late delivery.

We can proceed normally as follows:
If all vases delivered on time, amount collected --> 500 x $7.50 = $3750
$3750-$3675 = $75
$75 ÷ $25/6 = 18 --> 18 vases were delivered late.

To avoid with fractions, we can \"normalize\" the numbers -- $15 & $10, make multiple of 15 & 10 --> 30, 60, 90...- 60 is the ideal choice

So, Amount collected for 3 vases delivered late --> $10 -- 30 units ie $1 --> 3 units
Amount collected for 2 vases delivered on time --> $15 --- 45 units


So, amount collected for 1 vase delivered on time --> 22.5 units
amount collected for 1 vase delivered late --> 10 units


cheers.

[Winx5015]

Hi, got problem with math questions again . Sigh...


(1) Adrian, Ben and Calvin share 436 marbles. After Adrian gave away 2/5 of his marbles, the ratio of the number of marbles he has to Ben became 4:9. When Calvin lost 1/3 of his marbles, the total number of marbles the children has was 352. How many marbles did Calvin have at first?

(2) Jodie has 20% more red beads than green beads. She has 50 more orange beads than red beads. She mixed 20% of each of the coloured beads to make a total of 22 bracelets. She had used 298 red and orange beads for all the bracelets. How many beads were there in each bracelet?

Thanks

[MathIzzzFun]

Winx5015:

Hi, got problem with math questions again . Sigh...


(1) Adrian, Ben and Calvin share 436 marbles. After Adrian gave away 2/5 of his marbles, the ratio of the number of marbles he has to Ben became 4:9. When Calvin lost 1/3 of his marbles, the total number of marbles the children has was 352. How many marbles did Calvin have at first?

Thanks

Hi

After Adrian gave away 2/5 of his marbles :
Adrian's marbles : Ben's marbles --> 4 : 9 --> 12u : 27u --total 39u
Number given away by Adrian --> 8u

Calvin's marble --> 3p, lost --> 1p
Marbles given away & lost, 8u + 1p = 436-352 = 84 -- (1)
Marbles left, 39u + 2p = 352 ---(2)
Solving (1) & (2), 1u --> 8, 1p --> 20

Number of marbles Calvin had at first --> 3 x 20 = 60

cheers.

[MathIzzzFun]

Winx5015:

Hi, got problem with math questions again . Sigh...


(2) Jodie has 20% more red beads than green beads. She has 50 more orange beads than red beads. She mixed 20% of each of the coloured beads to make a total of 22 bracelets. She had used 298 red and orange beads for all the bracelets. How many beads were there in each bracelet?

Thanks

Hi
Red beads --> 60u, 20% --> 12u
Green beads --> 50u, 20% --> 10u
Orange beads --> 60u + 50, 20% --> 12u + 10
24u + 10 --> 298, 1u --> 12

Total beads used --> 298 + 10 x 12 = 418
Number of beads in each bracelet --> 418 / 22 = 19

cheers.

[anneshirleygilbert]

Hi MathIzzzFun,


I have some trouble interpreting this question:

The sum of 4 numbers is 80.If you add 3 to the first number, subtract 3 from the second number,multiply the third number by 3 d divide the fourth number by 3,the result will be equal.What is the difference between the largest and the smallest of the original numbers.

How do you interpret "the result will be equal"? You have made the end of each number equals 15, giving a total of 60. I interpreted it as the end total result is equal to the beginning total of 80 and got a mixed fraction answer. How do you know what’s the right way of interpreting the question? We get into such muddles sometimes. Pls help.


hi

Hi
after multiplying 3rd number by 3 –> 3u

1st number –> 3u-3
2nd number –> 3u +3
3rd number –> 1u
4th number –> 9u
Total –> 16u = 80
1u –> 5

1st number –> 12
2nd number –> 18
3rd number –> 5
4th number –> 45

cheers.

[Winx5015]

Hi MathIzzzFun, thank you and have a nice day

[MathIzzzFun]

anneshirleygilbert:

Hi MathIzzzFun,


I have some trouble interpreting this question:

The sum of 4 numbers is 80.If you add 3 to the first number, subtract 3 from the second number,multiply the third number by 3 d divide the fourth number by 3,the result will be equal.What is the difference between the largest and the smallest of the original numbers.

How do you interpret \"the result will be equal\"? You have made the end of each number equals 15, giving a total of 60. I interpreted it as the end total result is equal to the beginning total of 80 and got a mixed fraction answer. How do you know what's the right way of interpreting the question? We get into such muddles sometimes. Pls help.


hi

Hi
after multiplying 3rd number by 3 --> 3u

1st number --> 3u-3
2nd number --> 3u +3
3rd number --> 1u
4th number --> 9u
Total --> 16u = 80
1u --> 5

1st number --> 12
2nd number --> 18
3rd number --> 5
4th number --> 45

cheers.

\"If you add 3 to the first number, subtract 3 from the second number,multiply the third number by 3 d divide the fourth number by 3,the result will be equal\"--> my interpretation is:
1st number + 3
= 2nd number - 3
= third number x 3
= fourth number/3
= 3u (since the 3rd number was multiplied by 3)
so, this gives,
1st number --> 3u -3
2nd number --> 3u + 3
3rd number --> 3u/3 = 1u
4th number --> 3u x 3 = 9u

cheers.

[Shimmer]

1)At 9a.m, John was cycling from A to B . At the same time, Mary was cycling from Point B to A using the same route as John. Cycling at a speed of 4km/h faster than Mary, John would pass Mary 300 m away from midpoint.

A)What time did that pass each other?
B) If John took another 3 min to reach B, what time would Mary reach B?

[Shimmer]

In the 6A and B,the total number of girls was 100% more than boys. The ratio of boy to girl in 6A is 3:4 and the ratio of boy to girl in 6B is 1:6. If there were 8 more girls in 6a than 6b, find the no. of pupils in 6a.