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?
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 [tex]j- \frac{1}{6}j=45+h- \frac{1}{4}h [/tex] _______________ [tex](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[/tex]
Since Heather started with 120 stickers, Jared started with 162 stickers: j = 42 + h = 42 + 120 = 162
