QuestionQuestion \#15a: The ratio of boys to girls in the summer camp is 13:11. There are 120 more boys than girls. How many boys are in this camp? write numerical answer only

Studdy Solution

STEP 1

1. The ratio of boys to girls in the summer camp is 13:11.
2. There are 120 more boys than girls.
3. We need to find the number of boys in the camp.

STEP 2

1. Define variables based on the given ratio.
2. Set up an equation using the information about the difference in numbers.
3. Solve the equation to find the number of boys.

STEP 3

Define variables based on the given ratio. Let the number of boys be $13x$ and the number of girls be $11x$ .

STEP 4

Set up an equation using the information about the difference in numbers. According to the problem, there are 120 more boys than girls:
$13x = 11x + 120$

STEP 5

Solve the equation to find the number of boys.
Subtract $11x$ from both sides to isolate the variable term:
$13x - 11x = 120$ $2x = 120$
Divide both sides by 2 to solve for $x$ :
$x = \frac{120}{2}$ $x = 60$
Now, substitute $x = 60$ back into the expression for the number of boys:
$13x = 13 \times 60 = 780$
The number of boys in the camp is:
$\boxed{780}$

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