Question

The cost of 3 notebooks and 2 pens is $10.75. The cost of 4 notebooks and 6 pens is $23.50.

Part A: What is the cost of each item?

Part B: Waseem needs to purchase some new school supplies. For each notebook he buys he will buy 3 pens. How many notebooks can he purchase if he has $25?

Show your work and label your answers for both parts of this question.

Answer 1

Answer:

Part A

Let us consider, n to be mean price of notebook and p to be mean price of pen.

3n + 2p = 10.45 --------(1)

4n + 6p = 17.60 ---------(2)

Multiply Equations 1 by 3

9n + 6p = 31.35-----------(3)

Subtract equation (3) and (2)

9n + 6p = 31.35

-4n - 6p = -17.60

5n = 13.75

n = 2.75

Substitute n into either Equation (1) or (2) to get p

3(2.75) + 2p = 10.45

2p = 2.20

p = 1.10

Part B

Let us consider, m to be mean number of notebooks.

2.75m + 1.10 (3m) = 25

For example, if he buys 2 notebooks, he buys 3m = 6 pens.

2.75m + 3.30m = 25

6.05m = 25

m = 4.14

He must buy an integer number of notebooks that is less than or equal to 4.14

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