Question

cu 3-140. (from lesson 2.2.4)
andy likes to make candy sandwiches, where he takes
three gummy bears and puts them between two taffies.

a. what is the ratio of gummy bears to taffies in andy’s
candy sandwich?

b. write an equivalent ratio to the one you wrote in
part (a). how many candy sandwiches does this ratio
represent?

c. last week, andy’s ratio of gummy bears to taffies was
378:252. how many candy sandwiches did he eat?

Explanation:

Part (a)

Step1: Identify quantities

Gummy bears: 3, Taffies: 2.

Step2: Form ratio

Ratio of gummy bears to taffies is \( 3:2 \).

Step1: Multiply ratio by 2

Equivalent ratio: \( 3\times2:2\times2 = 6:4 \).

Step2: Determine sandwiches

Each sandwich needs 3 gummy bears and 2 taffies. For \( 6:4 \), \( 6\div3 = 2 \) sandwiches.

Step1: Simplify ratio

Divide \( 378:252 \) by GCD(378,252)=126. \( 378\div126 = 3 \), \( 252\div126 = 2 \). Ratio simplifies to \( 3:2 \), same as 1 sandwich.

Step2: Find number of sandwiches

Since \( 378\div3 = 126 \) (or \( 252\div2 = 126 \)).

Answer:

\( 3:2 \)

Part (b)