Question

The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the coordinate pair solution. *Round your answers to the hundredths (2 places past the decimal) with no spaces in the answer.

Answer 1

Let's denote the cost of an orange as $o and the cost of an apple as $a.

From the given information, we can set up the following system of equations:

12o + 7a = 5.36 ...(1)
8o + 5a = 3.68 ...(2)

To solve this system of equations, we can use the method of substitution. Rearranging equation (2) to solve for o, we get:

o = (3.68 - 5a)/8

Substituting this value of o in equation (1), we have:

12((3.68 - 5a)/8) + 7a = 5.36

Multiplying both sides by 8 to clear the fraction, we get:

12(3.68 - 5a) + 56a = 42.88

Distributing, we have:

44.16 - 60a + 56a = 42.88

Combining like terms, we get:

-4a = -1.28

Dividing both sides by -4, we find:

a = 0.32

Substituting this value of a back into equation (2), we have:

8o + 5(0.32) = 3.68

Simplifying, we get:

8o + 1.6 = 3.68

Subtracting 1.6 from both sides, we have:

8o = 2.08

Dividing both sides by 8, we find:

o = 0.26

Therefore, the cost of an orange is $0.26 and the cost of an apple is $0.32.

The coordinate pair solution is (0.26, 0.32).