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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?

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Answer:

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

Step-by-step 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

Answer:

The cost per pound of the oranges is $2.

The cost per pound of the bananas is $1.

Step-by-step 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 [tex]7x + 3y = 17[/tex].

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

This means that [tex]3x + 6y = 12[/tex].

So we have to solve the following system of equations:

[tex]7x + 3y = 17[/tex]

[tex]3x + 6y = 12[/tex]

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

[tex]-14x - 6y = -34[/tex]

[tex]-14x + 3x -6y + 6y = -34 + 12[/tex]

[tex]-11x = -22[/tex]

[tex]x = 2[/tex]

The cost per pound of the oranges is $2.

[tex]3x + 6y = 12[/tex]

[tex]3(2) + 6y = 12[/tex]

[tex]6y = 6[/tex]

[tex]y = 1[/tex]

The cost per pound of the bananas is $1.