Answer:
- orange: $0.44
- apple: $0.36
Step-by-step explanation:
Two equations for the purchase prices can be written. Let o and a represent the costs of an orange and an apple, respectively.
... 4o +5a = 3.56
... 3o +4a = 2.76
We can eliminate the o variable by subtracting 3 times the first equation from 4 times the second:
... 4(3o +4a) -3(4o +5a) = 4(2.76) -3(3.56)
... a = 0.36 . . . . simplify
This value can be substituted into either equation to find o. Let's use the first one.
... 4o +5·0.36 = 3.56
... 4o = 1.76 . . . . . . . . . subtract 1.80
... o = 0.44 . . . . . . . . . divide by 4
The cost of an orange is $0.44; the cost of an apple is $0.36.
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Comment on the solution
There are perhaps half a dozen different ways to solve a pair of linear equations in two variables. This method isn't necessarily the easiest, but it works. If you have a graphing calculator, quite often it includes matrix operations that will solve this quickly and easily.
