QuestionAt a school dance, the ratio of boys to girls is 4:5. With 72 students total, find the number of boys and girls.

Studdy Solution

STEP 1

Assumptions1. The ratio of boys to girls at the dance is45. The total number of students at the dance is723. The ratio represents the exact distribution of boys and girls at the dance

STEP 2

First, we need to find the total parts in the ratio. We can do this by adding the number of parts for boys and girls.
$Total\, parts = Boys\, parts + Girls\, parts$

STEP 3

Now, plug in the given values for the boys parts and girls parts to calculate the total parts.
$Total\, parts = +5$

STEP 4

Calculate the total parts in the ratio.
$Total\, parts =4 + =9$

STEP 5

Now that we have the total parts in the ratio, we can find the value of one part. This can be done by dividing the total number of students by the total parts in the ratio.
$Value\, of\, one\, part = Total\, students / Total\, parts$

STEP 6

Plug in the values for the total students and the total parts to calculate the value of one part.
$Value\, of\, one\, part =72 /9$

STEP 7

Calculate the value of one part.
$Value\, of\, one\, part =72 /9 =$

STEP 8

Now that we have the value of one part, we can find the number of boys at the dance. This can be done by multiplying the value of one part by the number of parts for boys.
$Number\, of\, boys = Value\, of\, one\, part \\times Boys\, parts$

STEP 9

Plug in the values for the value of one part and the boys parts to calculate the number of boys.
$Number\, of\, boys =8 \\times4$

STEP 10

Calculate the number of boys at the dance.
$Number\, of\, boys =8 \\times4 =32$

STEP 11

Similarly, we can find the number of girls at the dance. This can be done by multiplying the value of one part by the number of parts for girls.
$Number\, of\, girls = Value\, of\, one\, part \\times Girls\, parts$

STEP 12

Plug in the values for the value of one part and the girls parts to calculate the number of girls.
$Number\, of\, girls =8 \\times5$

STEP 13

Calculate the number of girls at the dance.
$Number\, of\, girls =8 \\times5 =40$ There are32 boys and40 girls at the dance.

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