Mathematics: 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?

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Jared has 42 more stickers than heather. jared

Ответ:

soccerjessie6846

14.01.2022

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
$j- \frac{1}{6}j=45+h- \frac{1}{4}h$
_______________
$(42+h)- \frac{1}{6}(42+h)=45+h- \frac{1}{4}h \\
 42+h- \frac{42}{6} - \frac{1}{6} h=45+ \frac{4}{4}h- \frac{1}{4}h \\ 
42+h-7- \frac{1}{6}h=45+ \frac{3}{4}h \\
42-7+ \frac{6}{6}h- \frac{1}{6}h=45+ \frac{3}{4}h \\ 
35+ \frac{5}{6}h = 45+\frac{3}{4}h \\
\frac{5}{6} h- \frac{3}{4} h=45-35 \\
 \frac{5*2}{6*2} h- \frac{3*3}{4*3} h=10
 \\ \frac{10}{12}h- \frac{9}{12}h=10 
\\ \frac{1}{12}h=10
 \\ h=10*12 \\ h = 120$

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

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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?

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