School choir

A school choir performed in 40 total competitions and lost 8. Gabrielle was a soloist in 3/8 of the winning competitions and 1/4 of the losing competitions.
What fraction of the competitions did the school choir win?
In how many competitions did Gabrielle have a solo?
Solve on paper.

Final Answer:

a =  4/5
b =  14

Step-by-step explanation:

$$\begin{gathered} n=40 \\ l=8 \\ w=n-l=40-8=32 \\ a=\frac{w}{n}=\frac{32}{40}=\frac{4}{5}=0.8 \end{gathered}$$

$$\begin{gathered} n_1=\frac{3}{8}\cdot w=\frac{3}{8}\cdot 32=\frac{3\cdot 32}{8}=\frac{96}{8}=12 \\ {n}_2=\frac{1}{4}\cdot l=\frac{1}{4}\cdot 8=\frac{1\cdot 8}{4}=\frac{8}{4}=2 \\ b=n_1+n_2=12+2=14 \end{gathered}$$

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