The ratio of boys to girls in a school is 9 to 11. After 36 more girls join, the ratio becomes 9 to 13. How many boys are there in the school?

Next, note the change in *ratio* in the girls column:
| | B | | G | |
|----------------|---|---|----|-----------|
| Original ratio | 9 | : | 11 | |
| Change | | | +2 | +36 girls |
| New Ratio | 9 | : | 13 | |
Use the
difference in *ratio* units and the corresponding change in *real* to find the multiplier.
Since a rise of 2 in the girls *ratio* (from 11 to 13) corresponds to a rise of 36 in the real values, the multiplier is simply $$\frac{36}{2} = \color{red}{18}$$
Use the multiplier to find the required quantity. Remember to use the ratios in their expanded/reduced form, rather than the original form.
The question asks for the number of boys, which is simply the original *ratio* of $$9 \cdot \color{red}{18} = \color{purple}{162}$$.

Incorrect.
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Carefully check your work.

Incorrect.
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Carefully check your work.

Incorrect.
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Carefully check your calculations.

Incorrect.
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You might have gotten this answer if you found the number of girls in the school after 36 more girls joined.

Correct.
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Compare the two ratios—expand/reduce so that the unchanged quantity is represented by the same number in *ratio*. Note the change in ratio units.
The common quantity in those ratios is the unchanged number of boys. The ratio units of the boys are already equal, so the ratios may be combined as is—no need to reduce/expand the ratios in order to compare them.

102

115

132

162

234

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