Answer:
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
Step-by-step 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.
