Sam had 250 erasers. ³₅ were black and the rest were white and yellow. The ratio of the number of white erasers to the number of yellow erasers was 1 : 4. Sam decided to give away some black erasers to decrease the number of black erasers to half of the total number of erasers.

1. How many more black erasers than white erasers did he have at first?
2. How many black erasers did he have to give away?

Black erasers	White erasers	Yellow erasers	Total
3x5	2x5
	1x2	4x2
15 u	2 u	8 u	250

	Black erasers	White erasers	Yellow erasers
Before	15 u	2 u	8 u
Change	- ?
After	10 u	10 u
Comparing black, white and yellow erasers in the end	1	1

(a)
The total number of white erasers and yellow erasers is repeated. Make the total number of white erasers and yellow erasers the same.  LCM of 2 and 5 is 10.

Total number of erasers at first
= 15 u + 2 u + 8 u
= 25 u

25 u = 250

1 u = 250 ÷ 25 = 10

Number of more black erasers than white erasers at first
= 15 u - 2 u
= 13 u
= 13 x 10
= 130

(b)
Number of more black erasers that Sam had to give away
= 15 u - 10 u
= 5 u
= 5 x 10
= 50

Answer(s): (a) 130; (b) 50