Lisa and Angeline like to share stickers. If Lisa gives 70 stickers to Angeline, the ratio of Lisa to Angeline's stickers will be 1 : 6. If Lisa gives 90 stickers to Angeline, their ratio will be 1 : 7. How many stickers does Lisa have?
Question
Lisa and Angeline like to share stickers. If Lisa gives 70 stickers to Angeline, the ratio of Lisa to Angeline's stickers will be 1 : 6. If Lisa gives 90 stickers to Angeline, their ratio will be 1 : 7. How many stickers does Lisa have?
Solution
To solve this problem, we can set up two equations based on the information given and then solve them simultaneously.
Let's denote the number of stickers Lisa has as L and the number of stickers Angeline has as A.
From the first condition, we know that if Lisa gives 70 stickers to Angeline, the ratio of Lisa to Angeline's stickers will be 1 : 6. This can be written as:
(L - 70) / (A + 70) = 1 / 6
From the second condition, we know that if Lisa gives 90 stickers to Angeline, their ratio will be 1 : 7. This can be written as:
(L - 90) / (A + 90) = 1 / 7
Now we have two equations and two unknowns, which we can solve simultaneously.
By cross-multiplying the first equation, we get:
6L - 420 = A + 70
Solving for A, we get:
A = 6L - 490
By cross-multiplying the second equation, we get:
7L - 630 = A + 90
Substituting A from the first equation into the second equation, we get:
7L - 630 = 6L - 490 + 90
Solving for L, we get:
L = 230
So, Lisa has 230 stickers.
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