Question

Mrs. Moore is making packages of art supplies for an art project. Each package contains sheets of white paper and blue paper. There are 84 sheets of blue paper and 96 sheets of white paper available to be used in the packages. Each package has the same number of blue paper. Each package has the same number of white paper. Mrs. Moore makes the maximum number of packages possible. There are no sheets of paper left over. What is the maximum number of packages that can be made and how many sheets of blue paper and white paper are in each package

Answer 1

The maximum number of packages that can be made are 12 packages

The number of sheets of blue paper and white paper per package = 7 and 8 sheets respectively

Explanation:

The number of sheets of blue paper available to Mrs. Moore = 84 sheets

The number of sheets of white paper available to Mrs. Moore = 96 sheets

The number of blue paper in each package = The number of white paper in each package

Therefore, the maximum number of packages that can be made is given by the Highest Common Factor, HCF, of 84 and 96 which is found as follows;

The prime factors of 84 = 2² × 3 × 7, from which we have;

Factors of 84 = 4 × 3 × 7 = 12 × 7

The prime factors of 96 = 2⁵ × 3, from which we have;

Factors of 96 = 4 × 8 × 3 = 12 × 8

∴ The HCF of 84 and 96 = 12

The maximum number of packages that can be made = Twelve packages

The number of sheets of blue paper in each package = Seven

The number of sheets of white paper in each package = Eight.