ms. tyson is doing an engineering challenge with her students. each team will get a kit with bags of…
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. which of the following numbers of identical kits can ms. tyson make? choose all that apply. 1 2 5 6 10 15
Answer
Explanation:
Step1: Find the GCD of 36 and 48
We need to find the greatest - common divisor (GCD) of 36 and 48. First, find the prime - factorizations of 36 and 48. The prime - factorization of 36 is $36 = 2^{2}\times3^{2}$. The prime - factorization of 48 is $48=2^{4}\times3^{1}$. The GCD is found by taking the lowest power of each common prime factor. The common prime factors are 2 and 3. For 2, the lowest power is 2, and for 3, the lowest power is 1. So, $GCD(36,48)=2^{2}\times3^{1}=12$. The number of identical kits must be a factor of both 36 and 48.
Step2: Check each option
- For 1: Since $36\div1 = 36$ and $48\div1 = 48$, 1 is a factor of both 36 and 48.
- For 2: Since $36\div2 = 18$ and $48\div2 = 24$, 2 is a factor of both 36 and 48.
- For 5: Since $36\div5=7.2$ and $48\div5 = 9.6$, 5 is not a factor of either 36 or 48.
- For 6: Since $36\div6 = 6$ and $48\div6 = 8$, 6 is a factor of both 36 and 48.
- For 10: Since $36\div10 = 3.6$ and $48\div10 = 4.8$, 10 is not a factor of either 36 or 48.
- For 15: Since $36\div15 = 2.4$ and $48\div15 = 3.2$, 15 is not a factor of either 36 or 48.
Answer:
- 1
- 2
- 6