Question

The ratio of the the number of Sally's stickers to the number of Eric's stickers was 3:5. Sally then brought another six stickers and the ratio became 9:10. How many stickers did Eric have?

Answer 1

Answer: Eric has 20 stickers

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Explanation:

x = number of stickers Sally starts with

y = number of stickers Eric has

x/y is the ratio of the two values. This ratio is 3/5. So x/y = 3/5 which cross multiplies to 5x = 3y. We can divide both sides by 5 to end up with x = 3y/5

"Sally the bought another six stickers" meaning she starts with x and bumps up to x+6. Eric's sticker count stays the same. The ratio is now (x+6)/y. We can replace the x with 3y/5 and simplify

(x+6)/y = (3y/5+6)/y

(x+6)/y = (3y/5+30/5)/y

(x+6)/y = [ (3y+30)/5 ]/y

(x+6)/y = (3y+30)/(5y)

Now set this equal to the new ratio 9/10 and solve for y

(3y+30)/(5y) = 9/10

10(3y+30) = 9(5y) ... cross multiply

30y+300 = 45y

300 = 45y-30y

300 = 15y

15y = 300

y = 300/15

y = 20

Eric has 20 stickers. At this point you can stop as your teacher doesn't seem to want to know Sally's count. However, I'll keep going to show how to get that value.

x = 3y/5

x = 3*20/5 ... replace y with 20

x = 60/5

x = 12

Sally starts off with 12 stickers. Note how x/y = 12/20 = 3/5 meaning that the ratio x:y = 12:20 reduces to 3:5 (divide both parts by 4)

If we add 6 stickers to Sally's count, then she now has x+6 = 12+6 = 18 stickers. It leads to the ratio 18:20 = 9:10 (divide both parts by 2). So the answer is confirmed.