Question

Jared has 42 more stickers than Heather. Jared gives away 1/6 of his stickers to his friends and Heather gives away 1/4 of her stickers to her cousins. Now Jared has 45 more stickers than Heather. How many stickers did Jared start with?

Answer 1

The answer is 162 stickers.

j - the number of Jared's stickers
h - the number of Heather's stickers

- Jared has 42 more stickers than Heather: j = 42 + h
- Jared gives away 1/6 of his stickers to his friends (j - 1/6j) and Heather gives away 1/4 (h - 1/4h) of her stickers to her cousins. Now Jared has 45 more stickers than Heather: j - 1/6j = 45 + h - 1/4h

We have two equations and we will use the substitution method:
j = 42 + h

`j- (1)/(6)j=45+h- (1)/(4)h`
_______________

`(42+h)- (1)/(6)(42+h)=45+h- (1)/(4)h \\ 42+h- (42)/(6) - (1)/(6) h=45+ (4)/(4)h- (1)/(4)h \\ 42+h-7- (1)/(6)h=45+ (3)/(4)h \\ 42-7+ (6)/(6)h- (1)/(6)h=45+ (3)/(4)h \\ 35+ (5)/(6)h = 45+(3)/(4)h \\ (5)/(6) h- (3)/(4) h=45-35 \\ (5*2)/(6*2) h- (3*3)/(4*3) h=10 \\ (10)/(12)h- (9)/(12)h=10 \\ (1)/(12)h=10 \\ h=10*12 \\ h = 120`

Since Heather started with 120 stickers, Jared started with 162 stickers:
j = 42 + h = 42 + 120 = 162