Question

An office supply store in San Diego sells 7 composition books and 3 pens for $22.50. Also, 2 composition books and 26 pens cost $36.60. Find the price of each.

Answer 1

Each pen costs $1.20

Each composition book costs $2.70

Explanation:

We can determine the price of each composition book and each pen using a system of equations, where:

• C represents the price of each composition book,
• and P represents the price of each pen.

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First equation:

Since 7 composition books and 3 pens cost $22.50, our first equation is given by:

7C + 3P = 22.50

Second equation:

Since 2 composition books and 26 pens cost $36.60, our second equation is given by:

2C + 26P = 36.60

Method to solve: Elimination:

Multiplying the first equation by 2 and the second equation by -7 will allow us to eliminate C when adding the two equations since 14C - 14C = 0:

Multiplying the first equation by 2:

2(7C + 3P = 22.50)

14C + 6P = 45.00

Multiplying the second equation by -7:

-7(2C + 26P = 36.60)

-14C - 182P = -256.20

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Solving for P (i.e., the price of each pen):

Now we can solve for P and eliminate C by adding 14C + 6P = 45.00 and -14C - 182P = -256.20

14C + 6P = 45.00

+

-14C - 182P = -256.20

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(14C - 14C) + (6P - 182P) = (45.00 - 256.20)

(-176P = -211.20) / -176

P = 1.20

Thus, each pen costs $1.20.

Solving for C (i.e., the price of each composition book):

Now, we can determine the price of each composition book by plugging in 1.20 for P in the first equation (i.e., 7C + 3P = 22.50):

7C + 3(1.20) = 22.50

(7C + 3.60 = 22.50) - 3.60

(7C = 18.90) / 7

C = 2.70

Thus, each composition book costs $2.70.