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Question 982088: Bob, Jack and Paul have 115 stickers altogether. The ratio of Bob's stickers to Jack's stickers is 5:4. The ratio of jack's stickers to Paul's stickers is 8:5. How many more stickers must Jack and Paul each buy so that the ratio of Bob's stickers to Jack's stickers to Paul's stickers is 5:6:7?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Bob, Jack and Paul have 115 stickers altogether.
Find how many stickers each guy has.
:
The ratio of Bob's stickers to Jack's stickers is 5:4.
let x = the multiplier for this ratio, then
5x = Bob's stickers
4x = Jack's stickers
:
The ratio of jack's stickers to Paul's stickers is 8:5.
let y - multiplier for this ratio
8y = Jack's stickers
5y = Paul's stickers
:
we know: 4x = 8y (Jack's stickers)
x = 8/4 y
x = 2y
:
"Bob, Jack and Paul have 115 stickers altogether. "
we can write this as:
5x + 8y + 5y = 115
Replace x with 2y
5(2y) + 8y + 5y = 115
10y + 8y + 5y = 115
23y = 115
y = 115/23
y = 5 is the 2nd multiplier
then
x = 2y
x = 2(5)
x = 10 is the first multiplier
:
Find the no. of stickers each has
Bob: 5(10) = 50 stickers
Jack: 4(10) = 40 stickers
Paul: 5(5) = 25 stickers
:
How many more stickers must Jack and Paul each buy so that the ratio of Bob's stickers to Jack's stickers to Paul's stickers is 5:6:7?
let z = the third multiplier
then:
5z = Bob's stickers, 50 stickers
5z = 50
z = 50/5
z = 10 is the multiplier
:
6z = Jack's stickers after buying some more
6(10) = 60 stickers total
:
7z = Paul's stickers after buying some more
7(10) = 70 stickers total
therefore
60 - 40 = 20 stickers bought by Jack
and
70 - 25 = 45 stickers bought by Paul
:
:
Check this; the final sticker numbers
50, 60, 70, which is 5:6:7
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