An office manager is ordering this year’s supply of pencils and pens for the office. Each pencil costs
$
0.10
,
each pen costs
$
0.75
,
and the manager will spend a total of
$
235
on pencils and pens.
Which additional piece of information is sufficient to determine the number of pencils and the number of pens that the manager will order?
A.
The number of pencils purchased last year will be equal to the number of pens purchased this year.
B.
The number of pens purchased this year will be three times the number of pencils purchased this year.
C.
The total cost of the pens purchased this year will be greater than the total cost of the pencils purchased this year.
D.
The total cost of the pencils and pens purchased last year will be three times the total cost of the pencils and pens purchased this year.
The answer is B. The number of pens purchased this year will be three times the number of pencils purchased this year.
Let's assign variables to the number of pencils and pens purchased this year. Let's say P represents the number of pencils and let's say Q represents the number of pens.
We know that each pencil costs $0.10 and each pen costs $0.75. The total cost of pencils is 0.10P and the total cost of pens is 0.75Q. We are also told that the total cost of pencils and pens is $235. So we have the equation 0.10P + 0.75Q = 235.
We also know that the number of pens purchased this year will be three times the number of pencils purchased this year. So we have the equation Q = 3P.
With these two equations, we can solve for the values of P and Q and determine the number of pencils and pens that the manager will order.