Question(4) Ms. Tyson is doing an engineering challenge with her students. Each team will get a kit with bags of marshmallows and boxes of toothpicks. Ms. Tyson has 36 bags of marshmallows and 48 boxes of toothpicks. She wants to use all the bags of marshmallows and all the boxes of toothpicks to make identical kits for the teams.
4. Which of the following numbers of identical kits can Ms. Tyson make? Choose ALL that apply.
Studdy Solution
STEP 1
1. Ms. Tyson has 36 bags of marshmallows.
2. Ms. Tyson has 48 boxes of toothpicks.
3. Each kit must have the same number of bags of marshmallows and boxes of toothpicks.
4. We need to determine the possible number of identical kits that can be made using all the bags and boxes.
STEP 2
1. Find the greatest common divisor (GCD) of the two quantities.
2. Determine all divisors of the GCD.
3. Identify which of these divisors can be the number of identical kits.
STEP 3
Find the GCD of 36 and 48.
- List the factors of 36: .
- List the factors of 48: .
STEP 4
Identify the common factors: .
STEP 5
The greatest common factor is .
STEP 6
Determine all divisors of the GCD, which is 12.
- The divisors of 12 are .
STEP 7
Identify which of these divisors can be the number of identical kits.
- Ms. Tyson can make or identical kits.
The possible numbers of identical kits Ms. Tyson can make are:
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