The ratio of black to red marbles in a bowl is 5 to 7. If eight more red marbles are added to the bowl, the ratio will become 5 to 9. How many black marbles are in the bowl?

Next, note the change in *ratio* in the red marbles column.
| | B | | R | |
|----------------|---|---|----|----------------|
| Original ratio | 5 | : | 7 | |
| Change | | | +2 | +8 red marbles |
| New Ratio | 5 | : | 9 | |
Use the difference in *ratio* units and the corresponding change in real values to find the multiplier.
Since a rise of 2 in the red marbles *ratio* (from 7 to 9) corresponds
to a rise of 8 in real values, the multiplier is simply $$\frac{8}{2} = \color{red}{4}$$.
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 black marbles, which is simply the original *ratio* of $$5 \cdot \color{red}{4} = \color{purple}{20}$$.

Incorrect.
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You might have gotten this answer if you calculated the number of red marbles in the bowl.

Incorrect.
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You might have gotten this answer if you made a mistake when calculating the multiplier.

Incorrect.
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Carefully check your work.

Incorrect.
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Carefully check your calculations.

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 black marbles. The ratio units of the black marbles are already equal,so the ratios may be combined as is—no need to reduce/expand the ratios in order to compare them.

10

16

20

25

36

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