The cost of 5 apples, 7 mangoes and 9 oranges is 184. The cost of 2 apples, 5 mangoes and 8 oranges is 144. What is the cost of 1 apple 1 orange and 1 mango?
Explanation:
Let the cost of 1 apple be a, cost of 1 mango be m and the cost of 1 orange be k
Then,
5a + 7m + 9k = 184 ...(1)
2a + 5m + 8k = 144 ...(2)
We can observe the difference between the coefficients in equations (1) and (2) are 2 and 3 respectively.
So, multiplying equation (1) by 3 and equation (2) by 2, we get:
15a + 21m + 27k = 552
4a + 10m + 16k = 288
Now subtracting the two equations gives:
11a + 11m + 11k = 264
⇒ a + m + k = 264/11
⇒ a + m + k = 24
Hence, option (d).
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