Question

The cost of 3 notebooks and 2 pens is $10.45. The cost of 4 notebooks and 6 pens is $17.60.

Part A: What is the cost of each item?

Part B: Miles 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 $22?

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

Answer 1

Notebooks cost $2.75 and pens cost $1.10.

He can also buy 3 notebooks.

Explanation:

In order to find this, we need to create two equations given each of the situations.

3n + 2p = 10.45

4n + 6p = 17.60

Now to solve for n, multiply the top equation by -3 and add together.

-9n - 6p = -31.35

4n + 6p = 17.60

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-5n = -13.75

n = 2.75

Now that we have the value of notebooks, we can find the amount for pens using either equation.

3n + 2p = 10.45

3(2.75) + 2p = 10.45

8.25 + 2p = 10.45

2p = 2.20

p = 1.10

Finally, to find the number of notebooks that he can purchase, find the cost of a notebook with 3 pens.

n + 3p

2.75 + 3(1.10)

2.75 + 3.30

6.05

Now divide 22 by that number

22/6.05 = 3.63

Since we can't have fractional notebooks, we round down to 3.