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The ratio boys : girls in a park is $1:4$ . $\newline$ $65$ girls leave and the ratio becomes $4:3$ . $\newline$ Work out how many boys there are in the park. $\newline$ $\square$ boys $\newline$

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Evaluate two-variable equations: word problems

Full solution

Q. The ratio boys : girls in a park is

1:4

.

\newline

65

girls leave and the ratio becomes

4:3

.

\newline

Work out how many boys there are in the park.

\newline

\square

boys

\newline

Initial Ratio Explanation: Initial ratio of boys to girls is $1:4$ . This means for every boy, there are $4$ girls. Let's denote the number of boys as $b$ and the number of girls as $4b$ .
New Ratio Calculation: After $65$ girls leave, the ratio changes to $4:3$ . The new number of girls is $4b - 65$ . The new ratio can be expressed as $\frac{b}{4b - 65} = \frac{4}{3}$ .
Equation Simplification: To find $b$ , we solve the equation $\frac{b}{4b - 65} = \frac{4}{3}$ . Cross-multiplying gives $3b = 4(4b - 65)$ .
Solving for $b$ : Simplifying the equation: $3b = 16b - 260$ . Then, $260 = 16b - 3b$ , $260 = 13b$ .
Final Number of Boys: Solving for $b$ , we get $b = \frac{260}{13}$ , $b = 20$ . So, there are $20$ boys in the park.

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