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QuestionAt a talent show, half the acts were musical. If three quarters of those were solos, what fraction were solo musical acts?

Studdy Solution

STEP 1

Assumptions1. The total number of acts in the talent show is represented as a whole or1. . Half of the acts were musical.
3. Three quarters of the musical acts were solo performances.

STEP 2

First, we need to express the fraction of the acts that were musical. This is given as one half.
Musical acts=12Musical\, acts = \frac{1}{2}

STEP 3

Next, we need to express the fraction of the musical acts that were solo performances. This is given as three quarters.
Solo musical acts=3Solo\, musical\, acts = \frac{3}{}

STEP 4

To find the fraction of the talent show that consisted of solo musical performances, we multiply the fraction of acts that were musical by the fraction of musical acts that were solo performances.
Fraction of solo musical acts=Musical actstimesSolo musical actsFraction\, of\, solo\, musical\, acts = Musical\, acts \\times Solo\, musical\, acts

STEP 5

Now, plug in the given fractions for the musical acts and the solo musical acts to calculate the fraction of solo musical acts.
Fraction of solo musical acts=12times34Fraction\, of\, solo\, musical\, acts = \frac{1}{2} \\times \frac{3}{4}

STEP 6

Calculate the fraction of solo musical acts.
Fraction of solo musical acts=12times34=38Fraction\, of\, solo\, musical\, acts = \frac{1}{2} \\times \frac{3}{4} = \frac{3}{8}The fraction of the talent show that consisted of solo musical performances is3/8.

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