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Ratios & Proportions: Ratio Changes by Addition/Subtraction

The ratio of boarders to day scholars at a school is 7 to 16. However, after a few new students join the initial 560 boarders, the ratio changed to 1 to 2, respectively. If no boarders became day scholars and vice versa, and no students left the school, how many boarders joined the school?
Correct. [[snippet]] The change in the boarders ratio is $$+1$$ (from 7 to 8). Use this to find the multiplier: the real number of original boarders divided by original boarders ratio is $$\frac{560}{7} = \color{red}{80}$$ Multiply this multiplier by the change in boarders ratio to find change in the number of boarders. >$$+1 \cdot \color{red}{80} = 80$$ Hence, the change of one unit in ratio corresponds to a change of $$+80$$ students in real. Therefore, this is the correct answer.
Incorrect. [[snippet]] You may have gotten this answer if you made a calculation error when finding the multiplier.
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
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