Joe bought 5 apples and 4 bananas for $6. Dawn bought 3 apples and 6 bananas for $6.30. How much does each apple and banana cost?

Question

“solve using a system of equations”

Answer 1

Let a equal the cost of the apples and b equal the cost of bananas. 

 

For Joe: 5a+4b=6
For Dawn: 3a+6b = 6.30

 

Let's solve for a in Dawn's equation:

3a+6b = 6.30
3a = 6.30 - 6b
a = 2.1 - 2b

 

Now let's plug that value for a in Joe's equation.

5a+4b=6
5(2.1-2b) + 4b = 6

10.5 - 10b + 4b = 6

4.5 - 10b + 4b = 0

4.5 + 4b = 10b
4.5 = 6b

0.75 = b

So, bananas cost $0.75
Plug that into either equation to solve for a.

 

5a+4(0.75)=6
5a+3=6
5a=3
a=1.67

 

So apples cost $1.67 each.

 

 

Answer 2

Let a = the cost of each apple

Let b = the cost of each banana

5a + 4b = 6        Multiply both sides by 3.

3a + 6b = 6.30   Multiply both sides by -5.

 15a + 12b = 18

-15a - 30b = -31.5

          -18b = -13.5

               b = $.75

5a + 4(.75) = 6.00

5a + 3 = 6.00

5a = 3.00

a = $.60