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Keddy, Cheko and Miko have saved some allowance to buy a gift for their teacher. Keddy and Cheko have $317. Keddy and Miko have $522. The ratio of Cheko to Miko's savings is 2 : 7. How much does Keddy have?

Question

Keddy, Cheko and Miko have saved some allowance to buy a gift for their teacher. Keddy and Cheko have 317.KeddyandMikohave317. Keddy and Miko have 522. The ratio of Cheko to Miko's savings is 2 : 7. How much does Keddy have?

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Solution

Step 1: Let's denote Keddy's savings as K, Cheko's savings as C, and Miko's savings as M.

Step 2: From the problem, we know that Keddy and Cheko together have 317,andKeddyandMikotogetherhave317, and Keddy and Miko together have 522. So we can write two equations:

K + C = 317 K + M = 522

Step 3: We also know that the ratio of Cheko to Miko's savings is 2 : 7. So we can write another equation:

C/M = 2/7

Step 4: We can solve the system of equations. First, subtract the first equation from the second to get:

M - C = 522 - 317 = 205

Step 5: Substitute C = 2M/7 into the equation from step 4 to get:

M - 2M/7 = 205 Multiply through by 7 to clear the fraction: 7M - 2M = 1435 5M = 1435 M = 1435 / 5 = 287

Step 6: Substitute M = 287 into the equation K + M = 522 to get:

K + 287 = 522 K = 522 - 287 = 235

So, Keddy has $235.

This problem has been solved

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