John and Ariana bought school supplies. John spent $10.50 on 4 notebooks and 7 pens. Ariana spent $7.50 on 3 notebooks and 4 pens. What is the cost of 1 notebook and what is the cost of 1 pen?

Cost of 1 notebook is $ 1.85 and cost of 1 pen is $ 0.65

Solution:

Let "a" be the cost of 1 notebook

Let "b" be the cost of 1 pen

Given that John spent $10.65 on 4 notebooks and 5 pens

cost of 1 notebook x 4 + cost of 1 pen x 5 = 10.65

4a + 5b = 10.65 eqn 1

Given that Ariana spent $7.50 on 3 notebooks and 3 pens

3a + 3b = 7.50 eqn 2

Let us solve eqn 1 and eqn 2 to get the values of "a" and "b"

Multiply eqn 1 with 3

12a + 15b = 31.95   eqn 3

Multiply eqn 2 with 4

12a + 12b = 30 eqn 4

Subtract eqn 4 from eqn 3

12a + 15b = 31.95

12a + 12b = 30

(-)

3b = 1.95

b = 0.65

Substitute b = 0.65 in eqn 1

4a + 5(0.65) = 10.65

4a = 7.4

a = 1.85

Thus cost of 1 notebook is $ 1.85 and cost of 1 pen is $ 0.65

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