Word problem help

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?

Answer 1

Part A

Use n to mean price of notebook. Use p to mean price of pen.

3n + 2p = 10.45 (1)

4n + 6p = 17.60 (2)

Multiply Equation (1) by 3

9n + 6p = 31.35

Take Eqn (3) minus Eqn. (2)

9n + 6p = 31.35

-4n - 6p = -17.60

5n = 13.75

n = 2.75

Part (B)

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

3(2.75) + 2p = 10.45

2p = 2.20

p = 1.10

Part (B)

Use N to mean NUMBER of notebooks (not the price)

2.75N + 1.10 (3N) <= 22 For example, if he buys 2 notebooks, he buys 3N = 6 pens.

2.75N + 3.30N <= 22.00

6.05N = 22.00

N <= 3.63

He must buy an integer number of notebooks that is less than or equal to 3.63

He can buy 3 notebooks and 9 pens.