17 apples and 12 oranges cost $10.44. 3 apples and 4 oranges cost $2.84. How much does 1 apple cost? How much does 1 orange cost?

Answer 1

Cost of 1 Apple = A

Cost of 1 Orange = O

17 apples and 12 oranges cost $10.44 equivalent to:

17A + 12O = 10.44 (1st equation).

3 apples and 4 oranges cost $2.84 equivalent to:

3A + 4O = 2.84 (2nd equation).

Now we have 2 equations and 2 unknowns need to find cost of 1 Apple and 1 Orange

17A + 12O = 10.44 (1st equation).

3A + 4O = 2.84 (2nd equation) multiplying this equation by 3 we get:

17A + 12O = 10.44 (1st equation)

9A + 12O = 8.52 (Equation 2), Now equation 2 minus equation 1 we get:

17A-9A +12O -12O = 10.44-8.52 equivalent to:

8A= 1.92 => A = 1.92/8 = 0.24 ( the cost of one Apple is 0.24$)

Go back to equation 1 and solve for the cost of 1 orange:

17*0.24 + 12O = 10.44 =>

12O + 4.08 = 10.44 =>

12O = 10.44-4.08 => 12O = 6.36

O = 6.36/12 = 0.53 ( the cost of one Orange is 0.53$)

Summary: The cost of one apple is 0.24$ and the cost of one orange is 0.53$.