Nanyang P5 EOY 2024 Word problem Q8
At first, Mary had 60 erasers and 85 pencils. After she gave away some erasers and 20%
of the pencils, she had a total of 118 erasers and pencils left.
How many erasers did Mary give away?
So, she gave away 17 pencils and had 85 - 17 = 68 pencils left.
After giving away some erasers and 17 pencils, she had a total of 118 erasers and pencils left. This means that the total number of erasers and pencils she had left is 118.
We know she had 68 pencils left, so the number of erasers she had left is 118 - 68 = 50 erasers.
Since she initially had 60 erasers, the number of erasers she gave away is 60 - 50 = 10 erasers.
Therefore, Mary gave away 10 erasers.
Sam read 35 pages more than 2/7 of his storybook. There were 175
pages left to be read.
a) What was the total number of pages in his storybook?
b) How many pages did Sam read?
a) Let's say the total number of pages in the storybook is x.
Sam read 2/7 of the storybook, which is (2/7)x pages. He also read 35 pages more than that, so the total number of pages he read is (2/7)x + 35.
Since there are 175 pages left to be read, the number of pages he read is the total number of pages minus 175, which is x - 175.
Setting up the equation, we get:
(2/7)x + 35 = x - 175
Multiplying both sides by 7 to eliminate the fraction, we get:
2x + 245 = 7x - 1225
Subtracting 2x from both sides, we get:
245 = 5x - 1225
Adding 1225 to both sides, we get:
1470 = 5x
Dividing both sides by 5, we get:
x = 294
b)
We already know that the total number of pages in the storybook is 294.
Sam read 2/7 of the storybook, which is (2/7) * 294 = 84 pages. He also read 35 pages more than that, so the total number of pages he read is 84 + 35 = 119 pages.
Therefore, Sam read 119 pages.
A factory worker packed 880 marbles into four boxes, A, B, C and D.
Box A had the greatest number of marbles and Box D had the least number of marbles.
The difference in the number of marbles between Box A and the number of marbles in the other three boxes were 14, 114 and 312.
a) Find the difference in the number of marbles between Box B and Box C.
b) How many marbles were there in Box D?
a) Let's denote the number of marbles in Box A as x.
The differences in the number of marbles between Box A and the other three boxes are given as:
x - Box B = 14
x - Box C = 114
x - Box D = 312
We can rewrite these equations as:
Box B = x - 14
Box C = x - 114
Box D = x – 312
Difference in number of marbles between Box B and Box C = (x-14) – (x-114) = 100
b) We know that the total number of marbles is 880, and the marbles are distributed among the four boxes. So, we can set up the equation:
x + (x - 14) + (x - 114) + (x - 312) = 880
Combine like terms:
4x - 440 = 880
Add 440 to both sides:
4x = 1320
Divide by 4:
x = 330
The number of marbles in Box D = 330 - 312 = 18