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
10 sets
7 sets
35 sets
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
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To find the greatest number of sets you can make, we need to determine how many complete sets can be made using both the pens and pencils without any leftovers.
1. Find the factors: We need to find the greatest common divisor (GCD) of the number of pens (28) and the number of pencils (80).
2. Calculate GCD:
– The prime factorization of 28 is (2^2 times 7).
– The prime factorization of 80 is (2^4 times 5).
– The common factor is (2^2).
– So, the GCD is (4).
3. Calculate the number of sets:
– Divide the total number of pens by the GCD: (28 div 4 = 7).
– Divide the total number of pencils by the GCD: (80 div 4 = 20).
Thus, you can make 7 sets using all pens and pencils equally.
Therefore, the correct answer is 7 sets.