Question

you are making sets of pens and pencils to sell. you want each set to contain the same combination of pens and pencils. you have 28 pens and 80 pencils, and you want to use them all. what is the greatest number of these sets you can make? 4 sets 7 sets 10 sets 35 sets

Explanation:

Step1: Find GCD of 28 and 80

Factorize 28: \(28 = 2 \times 2 \times 7\)
Factorize 80: \(80 = 2 \times 2 \times 2 \times 2 \times 5\)
Common factors: \(2 \times 2 = 4\)

Step2: Verify with sets

• 28 pens ÷ 4 sets = 7 pens/set
• 80 pencils ÷ 4 sets = 20 pencils/set

All items are used, so 4 sets work. Other options (7,10,35) don't divide both evenly.

Answer:

A. 4 sets