Tammy had 245 erasers. ³₇ were gold and the rest were purple and brown. The ratio of the number of purple erasers to the number of brown erasers was 1 : 4. Tammy decided to buy some more gold erasers to increase the number of gold erasers to half of the total number of erasers.

1. How many less purple erasers than gold erasers did he have at first?
2. How many more gold erasers did he have to buy?

Gold erasers	Purple erasers	Brown erasers	Total
3x5	4x5
	1x4	4x4
15 u	4 u	16 u	245

	Gold erasers	Purple erasers	Brown erasers
Before	15 u	4 u	16 u
Change	+ ?
After	20 u	20 u
Comparing gold, purple and brown erasers in the end	1	1

(a)
The total number of purple erasers and brown erasers is repeated. Make the total number of purple erasers and brown erasers the same.  LCM of 4 and 5 is 20.

Total number of erasers at first
= 15 u + 4 u + 16 u
= 35 u

35 u = 245

1 u = 245 ÷ 35 = 7

Number of less purple erasers than gold erasers at first
= 15 u - 4 u
= 11 u
= 11 x 7
= 77

(b)
Number of more gold erasers that Tammy had to buy
= 20 u - 15 u
= 5 u
= 5 x 7
= 35

Answer(s): (a) 77; (b) 35