Question

Mr. Briggs plans a package of pens and pencils for a back-to-school special. If pens sell for 39¢ each and pencils sell for three for 50¢, how many pens and pencils are in a set of sixteen writing instruments that sells for $3.56 per package?

A) 8 pens and 8 pencils
B) 4 pens and 12 pencils
C) 12 pens and 4 pencils
D) 10 pens and 6 pencils

Answer 1

To determine the composition of Mr. Briggs's back-to-school special package of 16 writing instruments, we set up equations based on the cost of pens and pencils and solved them to find that the package contains 4 pens and 12 pencils.

Step-by-step explanation:

To solve Mr. Briggs's back-to-school special pricing conundrum, we set up two equations to represent the total number of pens and pencils in a package and the total cost of these items. Since pens sell for 39¢ each and pencils sell for three for 50¢, we need to find a combination of pens and pencils totaling 16 items that equals $3.56 when purchased as a package.

Let's denote the number of pens as P and the number of pencils as L. We know that P + L = 16 (since there are a total of 16 writing instruments in a package). For the cost, each pen costs 39¢ and every three pencils cost 50¢, so for L pencils, we'd have L/3 groups of three pencils. The cost equation is thus 0.39P + (0.50)(L/3) = $3.56.

Multiplying through by 3 to get rid of the fraction we have: 1.17P + 0.50L = 10.68. Now we simplify our system of equations to solve for P and L.

1. P + L = 16
2. 1.17P + 0.50L = 10.68

We can multiply the first equation by 0.50 to have a new system:

1. 0.50P + 0.50L = 8
2. 1.17P + 0.50L = 10.68

Subtracting the first new equation from the second:

0.67P = 2.68

Divide both sides by 0.67 to find the number of pens:

P = 4

Using P = 4 in the original equation P + L = 16, we get:

L = 16 - 4

L = 12

Therefore, the package contains 4 pens and 12 pencils, which corresponds to option B.