Question

three sisters are saving for a special journey. the ratio of gertrudes savings to maurices savings is 7:2 and the ratio of maurices savings to helgas savings is 2:3. together all 3 sisters have saved $48. how much has each girl saved?
answer questions 3–4.

1. how can you use a diagram to make sense of the problem?

you can draw \\(\square\\) bar diagrams. gertrudes is \\(\square\\) squares long, maurices is \\(\square\\) squares long, and helgas is \\(\square\\) squares long. then, use the diagrams to show $\square$.
(type whole numbers.)

Explanation:

Step1: Unify the ratio

First, unify the ratios using Maurice's share as the common term. Gertrude:Maurice = 7:2, Maurice:Helga = 2:3, so Gertrude:Maurice:Helga = 7:2:3.

Step2: Calculate total parts

Add the ratio parts: $7 + 2 + 3 = 12$ parts

Step3: Find value per part

Total savings is $\$48$, so value per part is $\frac{48}{12} = 4$

Step4: Define diagram parameters

We need 3 bars (one per sister) with lengths matching their ratio parts (7, 2, 3), and each square represents $\$4$.

Answer:

You can draw 3 bar diagrams. Gertrude's is 7 squares long, Maurice's is 2 squares long, and Helga's is 3 squares long. Then, use the diagrams to show $\$4$.