QuestionFind the number of boys and girls in a chorus with a $3:8$ ratio, with totals of 11 last year and 33 this year.

Studdy Solution

STEP 1

Assumptions1. The boy-to-girl ratio is $38$ . The total number of chorus members last year was113. The total number of chorus members this year is33

STEP 2

We need to find the number of boys and girls for each year. We can do this by using the ratio and the total number of chorus members.
First, let's find the total parts in the ratio. $Total\, parts = Number\, of\, boys\, in\, ratio + Number\, of\, girls\, in\, ratio$

STEP 3

Plug in the given values for the number of boys and girls in the ratio to calculate the total parts in the ratio.
$Total\, parts =3 +8$

STEP 4

Calculate the total parts in the ratio.
$Total\, parts =3 +8 =11$

STEP 5

Now that we have the total parts in the ratio, we can find the number of boys and girls for each year.To do this, we multiply the number of boys and girls in the ratio by the total number of chorus members and then divide by the total parts in the ratio.
$Number\, of\, boys = (Number\, of\, boys\, in\, ratio \\times Total\, number\, of\, chorus\, members) / Total\, parts$ $Number\, of\, girls = (Number\, of\, girls\, in\, ratio \\times Total\, number\, of\, chorus\, members) / Total\, parts$

STEP 6

Plug in the values for the number of boys in the ratio, the total number of chorus members last year, and the total parts in the ratio to calculate the number of boys last year.
$Number\, of\, boys\, last\, year = (3 \\times11) /11$

STEP 7

Calculate the number of boys last year.
$Number\, of\, boys\, last\, year = (3 \\times11) /11 =3$

STEP 8

Plug in the values for the number of girls in the ratio, the total number of chorus members last year, and the total parts in the ratio to calculate the number of girls last year.
$Number\, of\, girls\, last\, year = (8 \\times11) /11$

STEP 9

Calculate the number of girls last year.
$Number\, of\, girls\, last\, year = (8 \\times11) /11 =8$

STEP 10

Plug in the values for the number of boys in the ratio, the total number of chorus members this year, and the total parts in the ratio to calculate the number of boys this year.
$Number\, of\, boys\, this\, year = (3 \\times33) /$

STEP 11

Calculate the number of boys this year.
$Number\, of\, boys\, this\, year = (3 \\times33) /11 =9$

STEP 12

Plug in the values for the number of girls in the ratio, the total number of chorus members this year, and the total parts in the ratio to calculate the number of girls this year.
$Number\, of\, girls\, this\, year = (8 \\times33) /11$

STEP 13

Calculate the number of girls this year.
$Number\, of\, girls\, this\, year = (8 \\times33) /11 =24$ So, last year there were3 boys and8 girls, and this year there are9 boys and24 girls.

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