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The ratio of boys to girls in a school is
9:11. If there are 400 pupils in the school, how many boys are there?
A. 80
B. 120
C. 180
D. 220

The ratio of boys to girls in a school is $9: 11$ . If there are $400$ pupils in the school, how many boys are there? $\newline$ A. $80$ $\newline$ B. $120$ $\newline$ C. $180$ $\newline$ D. $220$

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Exponential growth and decay: word problems

Full solution

Q. The ratio of boys to girls in a school is

9: 11

. If there are

400

pupils in the school, how many boys are there?

\newline

A.

80

\newline

B.

120

\newline

C.

180

\newline

D.

220

Denote Boys and Girls: Let's denote the number of boys as $B$ and the number of girls as $G$ . According to the problem, the ratio of boys to girls is $9:11$ , which can be written as $\frac{B}{G} = \frac{9}{11}$ .
Ratio and Total Number: We also know that the total number of pupils is the sum of the number of boys and girls, which is $B + G = 400$ .
Express in Terms of Ratio: To find the number of boys, we need to express both $B$ and $G$ in terms of the ratio $9:11$ . Let's introduce a variable $k$ such that $B = 9k$ and $G = 11k$ . This maintains the ratio of boys to girls.
Substitute in Equation: Now we can substitute $B$ and $G$ in the total number of pupils equation: $9k + 11k = 400$ .
Combine Like Terms: Combining like terms, we get $20k = 400$ .
Find Value of k: To find the value of k, we divide both sides of the equation by $20$ : $k = \frac{400}{20}$ .
Calculate k Value: Calculating the value of $k$ , we get $k = 20$ .
Find Number of Boys: Now that we have the value of $k$ , we can find the number of boys by substituting $k$ back into $B = 9k$ : $B = 9 \times 20$ .
Calculate Boys: Calculating the number of boys, we get $B = 180$ .

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