Best friends Olivia and Sylvia both get a weekly allowance. Olivia’s and Sylvia’s allowances are in the ratio 2:3 . If Sylvia gets $21 one week, how much did Olivia get? Use a tape diagram to help organize your thinking.(1 point)

Answer 1

To solve the problem using a tape diagram, we can represent the allowances of Olivia and Sylvia visually. The ratio of their allowances is 2:3, which means for every 2 parts that Olivia receives, Sylvia receives 3 parts.

1. Draw the Tape Diagram:
   • Create two sections in the tape diagram, one for Olivia and one for Sylvia.
   • Represent Olivia's allowance with 2 parts and Sylvia's allowance with 3 parts.

Olivia:  [---|---]   
            2 parts

Sylvia:   [---|---|---]   
            3 parts

2. Total Number of Parts:

   • The total number of parts in the ratio is \(2 + 3 = 5\) parts.

3. Value of Each Part:

   • We know Sylvia's allowance is $21, which corresponds to the 3 parts.
   • To find the value of one part, we divide Sylvia's allowance by the number of parts she represents: \[ \text{Value of one part} = \frac{21}{3} = 7 \]

4. Calculate Olivia's Allowance:

   • Now we can find Olivia's allowance, which is represented by 2 parts. \[ \text{Olivia's allowance} = 2 \times 7 = 14 \]

Thus, Olivia received $14 that week.