Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 18, 2024

What fraction of band students play the trumpet? Let $x$ be the total number of band students. Then $3/5$ of $x$ play brass, and $7/10$ of those play trumpet. The fraction of students playing trumpet is $(3/5)(7/10) = 21/50$ .

STEP 1

Assumptions
1. The fraction of students in the band who play a brass instrument is $\frac{3}{5}$ .
2. The fraction of students who play a brass instrument and also play the trumpet is $\frac{7}{10}$ .
3. We are looking for the fraction of all students in the band who play the trumpet.

STEP 2

To find the fraction of students in the band who play the trumpet, we need to multiply the fraction of students who play a brass instrument by the fraction of those brass instrument players who play the trumpet.
$Fraction\, of\, trumpet\, players = Fraction\, of\, brass\, instrument\, players \times Fraction\, of\, brass\, players\, who\, play\, the\, trumpet$

STEP 3

Now, plug in the given values for the fractions to calculate the fraction of students who play the trumpet.
$Fraction\, of\, trumpet\, players = \frac{3}{5} \times \frac{7}{10}$

STEP 4

Multiply the numerators together and the denominators together to find the fraction of students who play the trumpet.
$Fraction\, of\, trumpet\, players = \left(\frac{3}{5}\right) \times \left(\frac{7}{10}\right) = \frac{3 \times 7}{5 \times 10}$

STEP 5

Calculate the product of the numerators and the product of the denominators.
$Fraction\, of\, trumpet\, players = \frac{3 \times 7}{5 \times 10} = \frac{21}{50}$
The fraction of the students in the band who play the trumpet is $\frac{21}{50}$ .

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