Question

Tommy has to buy some pens, pencils and notebooks for the upcoming semester. He has

$102 to spend on $5 pens, $3 pencils, and $9 notebooks. He would like to spend the same
amount of money on pens as on pencils. He also wants the combined number of pens and
pencils to be equal to that of notebooks.
How many of each item should he buy? Write a system of equations to help you solve this
problem.
Pens = X=
Pencils = P =
Notebooks = N =

Answer 1

He should buy

Pens = 3

Pencils = 5

Notebooks = 8

Explanation:

Let

Pens = x

Pencils = p

Notebooks = n

Cost of

Pens = $5

Pencils = $3

Notebook = $9

Total cost = $102

5x = 3p

5x + 3p + 9n = 102

x + p = n

5x + 3p + 9(x+p) = 102

5x + 3p + 9x + 9p = 102

Substitute 5x for 3p

5x + 5x + 9x + 9p = 102

If 5x = 3p , then 15x = 9p

Substitute 15x for 9p

5x + 5x + 9x + 15x = 102

31x = 102

x = 102/34

= 3

x = 3

Substitute x= 3 into

5x = 3p

5(3) = 3p

15 = 3p

Divide both sides by 3

p = 15/3

=5

p = 5

Substitute the values of p and x into

x + p = n

3 + 5 = n

8 = n

n = 8

Therefore,

Pens = x = 3

Pencils = p = 5

Notebooks = n = 8