MO Z7 2025

Adela and Susan ate plums. On the first day, Adela ate three quarters of what Susan ate that day. On the second day, Susan ate three halves of what Adela ate that day. Together, they ate 31 plums over the two days, and each girl ate the entire number of plums each day. How many plums did Adela eat over the two days?

Final Answer:

A =  13

Step-by-step explanation:

$$\begin{gathered} a_1=\frac{3}{4}\cdot z_1 \\ {z}_2=\frac{3}{2}\cdot a_2 \\ {a}_1+a_2+z_1+z_2=31 \\ \frac{3}{4}\cdot z_1+a_2+z_1+\frac{3}{2}\cdot a_2=31 \\ 3z_1+4a_2+4z_1+3\cdot 2\cdot a_2=31\cdot 4 \\ 7z_1+10a_2=124 \\ {z}_1=2 \\ {a}_2=11 \\ {z}_1=12 \\ {a}_2=4 \\ {a}_1=\frac{3}{4}\cdot z_1=\frac{3}{4}\cdot 12=\frac{3\cdot 12}{4}=\frac{36}{4}=9 \\ {z}_2=\frac{3}{2}\cdot a_2=\frac{3}{2}\cdot 4=\frac{3\cdot 4}{2}=\frac{12}{2}=6 \\ A=a_1+a_2=9+4=13 \\ \text{ Verifying Solution: } \\ s=a_1+a_2+z_1+z_2=9+4+12+6=31 \end{gathered}$$

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