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The ratio boys : girls in a park is \newline1:41:4\newline6565 girls leave and the ratio becomes \newline4:34:3\newlineWork out how many boys there are in the park.\newline□\square boys\newlineSubmit Answer

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Q. The ratio boys : girls in a park is \newline1:41:4\newline6565 girls leave and the ratio becomes \newline4:34:3\newlineWork out how many boys there are in the park.\newline□\square boys\newlineSubmit Answer
  1. Initial Ratio Explanation: Initial ratio of boys to girls is 1:41:4. This means for every boy, there are 44 girls. Let's denote the number of boys as bb and the number of girls as 4b4b.
  2. New Ratio Calculation: After 6565 girls leave, the ratio changes to 4:34:3. The new number of girls is 4b−654b - 65. The new ratio can be expressed as b4b−65=43\frac{b}{4b - 65} = \frac{4}{3}.
  3. Equation Simplification: To find bb, we solve the equation b4b−65=43\frac{b}{4b - 65} = \frac{4}{3}. Cross-multiplying gives 3b=4(4b−65)3b = 4(4b - 65).
  4. Solving for bb: Simplifying the equation: 3b=16b−2603b = 16b - 260. Then, 260=16b−3b260 = 16b - 3b, 260=13b260 = 13b.
  5. Final Number of Boys: Solving for bb, we get b=26013b = \frac{260}{13}, b=20b = 20. So, there are 2020 boys in the park.

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