This friends Olivia and Sara both get a weekly allowance. Olivia and Sara allowances are in the radio 2:3 if Sarah gets 21 how much did Aaliyah get use a tape diagram to help organize your thinking?

1 answer

To solve the problem, let's first understand the ratio of Olivia's to Sara's allowances, which is 2:3. This means for every 2 parts that Olivia receives, Sara receives 3 parts.

  1. Identify Sara's allowance: According to the problem, Sara's allowance is 21. We can set up the ratio using Sara's allowance. Since Sara's part of the ratio is 3 parts, we can represent her allowance as: \[ \text{Sara's allowance} = 3x \] where \( x \) is the value of one part in the ratio.

    Since we know that Sara gets 21, we can write: \[ 3x = 21 \]

  2. Solve for \( x \): To find \( x \): \[ x = \frac{21}{3} = 7 \]

  3. Find Olivia's allowance: According to the ratio, Olivia receives 2 parts. Therefore, her allowance can be represented as: \[ \text{Olivia's allowance} = 2x \] Substitute \( x \): \[ \text{Olivia's allowance} = 2 \times 7 = 14 \]

  4. Conclusion:

    • Sara's allowance is 21.
    • Olivia's allowance is 14.

Therefore, Aaliyah does not appear in this context, and the amount that Olivia gets is 14.

Tape Diagram Visualization:

You could visualize it with a tape diagram as follows:

  • Draw a rectangle divided into 5 equal parts (since 2 (Olivia) + 3 (Sara) = 5)
  • Label the first 2 parts as "Olivia" which would equal \( 2 \times 7 = 14 \)
  • Label the last 3 parts as "Sara" which would equal \( 3 \times 7 = 21 \)

This diagram demonstrates how the two allowances correspond to a total of 5 parts, illustrating the ratio of allowances clearly.