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Su Lin and Dawn shared some cakes in the ratio 1 : 4. If Dawn bought another 112 cakes, the new ratio of Su Lin's cakes to Dawn's cakes would be 4 : 17. How many cakes did Su Lin have?

Question

Su Lin and Dawn shared some cakes in the ratio 1 : 4. If Dawn bought another 112 cakes, the new ratio of Su Lin's cakes to Dawn's cakes would be 4 : 17. How many cakes did Su Lin have?

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Solution

Let's solve this problem step by step:

Step 1: Let's assume the number of cakes Su Lin and Dawn initially had were 1x and 4x respectively.

Step 2: According to the problem, Dawn bought another 112 cakes. So, the number of cakes Dawn has now is 4x + 112.

Step 3: The problem also states that the new ratio of Su Lin's cakes to Dawn's cakes is 4 : 17. So, we can write this as a proportion: 1x/4x = 4/17.

Step 4: Solving this equation gives us x = 68.

Step 5: So, Su Lin initially had 1x = 1*68 = 68 cakes.

This problem has been solved

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