Cheko and Keddy like to share stickers. If Cheko gives 30 stickers to Keddy, the ratio of Cheko to Keddy's stickers will be 1 : 7. If Cheko gives 40 stickers to Keddy, their ratio will be 1 : 11. How many stickers does Cheko have?
Question
Cheko and Keddy like to share stickers. If Cheko gives 30 stickers to Keddy, the ratio of Cheko to Keddy's stickers will be 1 : 7. If Cheko gives 40 stickers to Keddy, their ratio will be 1 : 11. How many stickers does Cheko have?
Solution
Let's denote the number of stickers Cheko has as C and the number of stickers Keddy has as K.
From the problem, we have two equations based on the ratios given:
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If Cheko gives 30 stickers to Keddy, the ratio of Cheko to Keddy's stickers will be 1 : 7. This can be written as: (C - 30) / (K + 30) = 1 / 7.
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If Cheko gives 40 stickers to Keddy, their ratio will be 1 : 11. This can be written as: (C - 40) / (K + 40) = 1 / 11.
Now we have a system of two equations, and we can solve it step by step.
First, let's multiply each equation by the denominators to get rid of the fractions:
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7 * (C - 30) = K + 30, which simplifies to 7C - 210 = K + 30.
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11 * (C - 40) = K + 40, which simplifies to 11C - 440 = K + 40.
Now we have two new equations:
- 7C - K = 240
- 11C - K = 480
Subtract the first equation from the second:
11C - 7C = 480 - 240 4C = 240 C = 240 / 4 C = 60
So, Cheko has 60 stickers.
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