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QuestionThe choir has a girls-to-boys ratio of 4:34:3. After adding 6 girls and 9 boys, the ratio becomes 17:1517:15. Find the original number of girls.

Studdy Solution

STEP 1

Assumptions1. The original ratio of the number of girls to boys in the choir is43. . After6 girls and9 boys join, the ratio becomes1715.
3. We are to find the original number of girls in the choir.

STEP 2

Let's denote the original number of girls as 4x4x and the original number of boys as xx, where xx is a positive integer representing the common multiplier for the ratio.

STEP 3

After6 girls and9 boys join the choir, the number of girls becomes x+6x +6 and the number of boys becomes 3x+93x +9.

STEP 4

We know that the new ratio of girls to boys is1715. So, we can set up the following equation4x+63x+9=1715\frac{4x +6}{3x +9} = \frac{17}{15}

STEP 5

Cross multiply to simplify the equation.
(4x+)×15=(3x+9)×17(4x +) \times15 = (3x +9) \times17

STEP 6

Expand both sides of the equation.
60x+90=51x+15360x +90 =51x +153

STEP 7

Rearrange the equation to isolate xx on one side.
60x−51x=153−9060x -51x =153 -90

STEP 8

implify the equation.
x=63x =63

STEP 9

olve for xx.
x=639=7x = \frac{63}{9} =7

STEP 10

Now that we have the value of xx, we can find the original number of girls, which is 4x4x.
Number of girls=4x\text{Number of girls} =4x

STEP 11

Substitute x=7x =7 into the equation.
Number of girls=4×7\text{Number of girls} =4 \times7

STEP 12

Calculate the original number of girls.
Number of girls=4×7=28\text{Number of girls} =4 \times7 =28The original number of girls in the choir was28.

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