# 1.Six pears and three apples cost \$3.90. Two pears and five apples cost \$3.30. How much does one pear cost?

Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations.

6P + 3A=3.90
2P + 5A=3.30

Solve. I will be happy to critique your work.

HERE IS WHAT I GOT:A=.90

No, that is not right. Where is your work?

## To solve this problem using a system of equations, let's represent the cost of one pear as P and the cost of one apple as A. We can set up the following system of equations based on the given information:

Equation 1: 6P + 3A = 3.90
Equation 2: 2P + 5A = 3.30

To solve this system, we can use the method of substitution or elimination. Let's use substitution:

From Equation 1, solve for P:
6P = 3.90 - 3A
P = (3.90 - 3A) / 6

Now substitute this expression for P into Equation 2:
2((3.90 - 3A) / 6) + 5A = 3.30

Let's simplify this equation:
(7.80 - 6A) / 6 + 5A = 3.30
Multiply both sides by 6 to eliminate the denominator:
7.80 - 6A + 30A = 19.80

Combine like terms:
24A = 12

Divide both sides by 24:
A = 0.50

Now substitute this value of A back into Equation 1 to find P:
6P + 3(0.50) = 3.90
6P + 1.50 = 3.90
6P = 3.90 - 1.50
6P = 2.40
P = 2.40 / 6
P = 0.40

Therefore, the cost of one pear is \$0.40.