Question

Nancy bought 7 pounds of oranges and 3 pounds of bananas for $17. Her husband later bought 3 pounds of oranges and 6 pounds of bananas for $12. What was the cost per pound of the oranges and the bananas?

Answer 1

The cost per pound of the oranges is $2.

The cost per pound of the bananas is $1.

Explanation:

This problem can be solved by a simple system of equations.

I am going to say that:

x is the value of the pound of orange

y is the value of the pound of banana.

Lets build the system:

Nancy bought 7 pounds of oranges and 3 pounds of bananas for $17.

This means that
`7x + 3y = 17`.

Her husband later bought 3 pounds of oranges and 6 pounds of bananas for $12.

This means that
`3x + 6y = 12`.

So we have to solve the following system of equations:

`7x + 3y = 17`

`3x + 6y = 12`

I am going to solve this by the addition method, multiplying the first equation by minus two and adding with the second. So

`-14x - 6y = -34`

`-14x + 3x -6y + 6y = -34 + 12`

`-11x = -22`

`x = 2`

The cost per pound of the oranges is $2.

`3x + 6y = 12`

`3(2) + 6y = 12`

`6y = 6`

`y = 1`

The cost per pound of the bananas is $1.

Answer 2

The price of oranges is US$ 2 per pound and the price of bananas is US$ 1 per pound.

Explanation:

1. Bananas and oranges bought by Nancy:

Oranges = 7 pounds

Bananas = 3 pounds

Cost = US$ 17

2. Bananas and oranges bought by Nancy's husband:

Oranges = 3 pounds or 3x

Bananas = 6 pounds or 6y

Cost = US$ 12

3x + 6y = 12 (Dividing by 3 at both sides of the equation)

x + 2y = 4

x = 4 - 2y

3. Total Purchases:

Oranges = 10 pounds or 10x

Bananas = 9 pounds or 9y

Cost = US$ 29

10x + 9y = 29

10 (4 - 2y) + 9y = 29 (Replacing x with 4 - 2y from 2nd purchase)

40 - 20y +9y = 29

-11y = 29 - 40

- 11y = - 11

y = 1 (Dividing by -11 at both sides)

Pound of bananas = US$ 1

10x + 9 (1) = 29 (Replacing y by 1 in the original formula)

10x + 9 = 29

10x = 20

x = 2 (Dividing by 10 at both sides)

Pound of oranges = US$ 2