Question

bonnie volunteers to bring bags of candy to her childs class for the halloween party this year. she buys one bag of candy a containing 72 pieces of candy, one bag of candy b containing 120 pieces of candy, and one bag of candy c containing 48 pieces of candy. she needs to use all the candy to create identical treat bags. how many treat bags can bonnie make so that each one has the same number and variety of candy? how many of each type of candy will be in each bag?

no. of identical treat bags:
no. of pieces of candy a:
no. of pieces of candy b:
no. of pieces of candy c:

Explanation:

Identify the given values

We have three quantities of candy:

• Candy A: 72 pieces
• Candy B: 120 pieces
• Candy C: 48 pieces

Find the greatest common factor

Using the Greatest Common Factor knowledge point, we find the largest number of identical bags that can be made. This is the greatest common divisor (GCD) of 72, 120, and 48.

• Prime factorization of 72:

$$72 = 2^3 \times 3^2$$

• Prime factorization of 120:

$$120 = 2^3 \times 3 \times 5$$

• Prime factorization of 48:

$$48 = 2^4 \times 3$$

• The common prime factors are 2 and 3. Taking the lowest power of each:

$$\text{GCD}(72, 120, 48) = 2^3 \times 3 = 24$$

Calculate candy per bag

Divide each candy total by the number of bags (24) to find the amount of each candy type in each bag:

• Candy A:

$$\frac{72}{24} = 3$$

• Candy B:

$$\frac{120}{24} = 5$$

• Candy C:

$$\frac{48}{24} = 2$$

Answer:

Bonnie volunteers to bring bags of candy to her child's class for the Halloween party this year. She buys one bag of candy A containing 72 pieces of candy, one bag of candy B containing 120 pieces of candy, and one bag of candy C containing 48 pieces of candy. She needs to use all the candy to create identical treat bags. How many treat bags can Bonnie make so that each one has the same number and variety of candy? How many of each type of candy will be in each bag?

No. of identical treat bags: <blank>24</blank>

No. of pieces of candy A: <blank>3</blank>

No. of pieces of candy B: <blank>5</blank>

No. of pieces of candy C: <blank>2</blank>