Question

Francis works at Carlos Bakery and is making cookie trays. She has 48 chocolate chip cookies, 64 rainbow cookies, and 120 oatmeal cookies to put on the trays. Part A: How many trays can Francis make under the following condition? Part B: How many of each type of cookie would fit on each of the trays? Justify your answer.
48 chocolate chip cookies = 1 batch

64 rainbow cookies = 1 batch

120 oatmeal cookies = 1 batch
What are the smallest number of batches of each type of cookie she would need to bake so that Francis has the same amount of chocolate chip, rainbow, and oatmeal cookies?

Answer 1

The number of cookies and trays are illustrations of greatest common factors.

• The number of trays is 8
• 6 chocolate chips, 8 rainbows and 15 oatmeal cookies would fit each tray

The given parameters are:

$\mathbf{Chocolate\ chip=48}$

$\mathbf{Rainbow=64}$

$\mathbf{Oatmeal=120}$

(a) The number of trays

To do this, we simply calculate the greatest common factor of 48, 64 and 120

Factorize the numbers, as follows:

$\mathbf{48 = 2 \times 2 \times 2 \times 2 \times 3}$

$\mathbf{64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2}$

$\mathbf{120 = 2 \times 2 \times 2 \times 3 \times 5}$

So, the GCF is:

$\mathbf{GCF= 2 \times 2 \times 2}$

$\mathbf{GCF= 8}$

Hence, the number of tray is 8

(b) The number of each type of cookie

We have

$\mathbf{Chocolate\ chip=48}$

$\mathbf{Rainbow=64}$

$\mathbf{Oatmeal=120}$

Divide each cookie by the number of trays

So, we have:

$\mathbf{Chocolate\ chip = \frac{48}{8} = 6}$

$\mathbf{Rainbow = \frac{64}{8} = 8}$

$\mathbf{Oatmeal = \frac{150}{8} = 15}$

Hence, 6 chocolate chips, 8 rainbows and 15 oatmeal cookies would fit each tray

Read more about greatest common factors at:

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