Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive. He wants each bag to have the same amount of pasta and sauce and wants to use all of the items.
Use the drop-down menus to complete the statements below about the number of bags Cesar can make.
The greatest number of bags Cesar can make is . Each of these bags will have boxes of pasta and jars of sauce.
If he made fewer bags, .
He could use bags, but this is not the greatest number he could use.
To determine the greatest number of bags that Cesar can make, we need to find the greatest common divisor (GCD) of the number of boxes of pasta and jars of sauce he has.
1. Finding the GCD:
– The numbers are 32 (boxes of pasta) and 48 (jars of sauce).
– The factors of 32 are: 1, 2, 4, 8, 16, 32.
– The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
– The common factors are: 1, 2, 4, 8, 16.
– The greatest common factor is 16.
2. Calculating the number of bags:
– If the GCD is 16, this means Cesar can make a maximum of 16 bags.
– Each of these bags will contain:
– Pasta: 32 boxes ÷ 16 bags = 2 boxes of pasta per bag.
– Sauce: 48 jars ÷ 16 bags = 3 jars of sauce per bag.
Now, let’s put this information into the statements:
– The greatest number of bags Cesar can make is 16. Each of these bags will have 2 boxes of pasta and 3 jars of sauce.
– If he made