Question

A hardware store sells power pack A, consisting of 4 D cells and 2 C cells for $12.60, and power pack B, consisting of 6 D cells and 4 C cells for $20.80. What is the price of each cell?

Answer 1

C = $1.90 each

D = $2.20 each

Explanation:

Given:

Power pack A: 4D + 2C = 12.60

Power pack B: 6D + 4C = 20.80

Isolate any one variable:

4D + 2C = 12.60

4D = 12.60 - 2C

D = 3.15 - 0.5C

Substitution to find cost of C cell battery:

6D + 4C = 20.80

6(3.15 - 0.5C) + 4C = 20.80

18.9 - 3C + 4C = 20.80

18.9 + C = 20.80

C = 1.90

Substitution to find cost of D cell battery:

4D + 2C = 12.60

4D + 2(1.90) = 12.60

4D + 3.8 = 12.60

4D = 8.8

D = 2.20

Answer 2

The D cells are worth $2.20, and the C cells are worth $1.90.

Explanation:

This can be written as:

4x + 2y = 12.60

6x + 4y =20.80

Our goal is to find one variable, then use that information to find the other.

If we multiply the top function by -1.5, we get:

-6x - 3y = -18.90

We can add this to the previous equation.

-6x - 3y = -18.90

+ 6x + 4y = 20.80

--------------------------

y = 1.90

The C cells are worth $1.90.

Plug this value into one of the other equations and solve for x.

4x + 2y = 12.60

4x + 2(1.90) = 12.60

4x + 3.80 = 12.60

4x = 8.80

x = 2.20

The D cells are worth $2.20.

Check these values in the other equation.

6x + 4y = 20.80

6(2.20) + 4(1.90) = 20.80

13.20 + 7.60 = 20.80

20.80 = 20.80