Jeremy bought 8 bananas and 5 apples at the store and spent $10.10 total. Vorris bought 5 bananas and 6 apples and spent $8.90 at the same store.

Question

Bananas cost $ ? (each)

.Apples cost $ ? (each)

Answer 1

Set up a system of equations to solve for the price of apples and bananas. Use the variable "a" for apples, and "b" for bananas.

The equation for Jeremy: 5a + 8b = 10.10.

The equation for Vorris: 6a + 5b = 8.90.

Using the elimination method, and causing a variable to be eliminated, is one way to solve. You could choose either "a" or "b" to eliminate. I choose "a." I want it to "disappear" when I add the equations together, so I will need to manipulate both equations (do something to them) to make the 5a and 6a add up to zero. The lowest common multiple of 5 and 6 is 30, so I will multiple Jeremy's equation through by --6 (be sure it's negative). That will make the term with the "a" in it become --30a. Vorris's equation will be multiplied by 5, to make the "a" term come up to 30a. See the manipulated equations below.

–30a -48b = —60.60

30a + 25b = 44.50

We line both equations up so we can now add them together.

–30a -48b = —60.60

30a + 25b = 44.50

The sum of the two equations gives us: —23b = —16.10. Solve for b by dividing both sides by —23. You will get b = 0.70 for the price of the bananas.

To find the price of the apples, put the value for b (0.70) into either of your original equations. Either one will work. For example: 5a + 8(0.70) = 10.10 uses the top equation. Solve this equation for a and you get 0.90.

Price of apples: $ 0.90 each

Price of bananas: $ 0.70 each

These answers can be check by putting them back into either equation and ensuring that you have an equal amount on both sides.

5(0.90) + 8(0.70) = 10.10

4.5 + 5.6 = 10.10

10.10 = 10.10

The answers check.

Answer 2

Hi Georgina S

Bananas cost $0.70

Apples cost $0.90

I used a system of equations and elimination below, you can also use substitution

b = bananas

a = apples

Equation 1 for Jeremy

8b + 5a = 10.10

Equation 2 for Vorris

5b + 6a = 8.90

Multiply Equation 1 by 6

Multiply Equation 2 by negative 5

48b + 30a = 60.60

-25b - 30a = -44.50

Combine the equations above to eliminate a

23b = 16.10

Divide both sides by 23 to solve for b

b = 0.7

Plug 0.7 in for b in the Original Equation 1 to solve for a

8(0.7) + 5a = 10.10

5.6 + 5a = 10.10

Subtract 5.6 from both sides of the Equation

5a = 4.50

Divide both sides bt 5

a = 0.9

Check both values in the Original Equation 2

5(0.7) + 6(0.9) = 8.90

3.50 + 5.40 = 8.90

I hope this helps, remember you can also try substitution please send me a message if you have any questions