Write the statement as a proportion.
99 people is to 90 chairs as 11 people is to 10 chairs
A) $\frac { 11 } { 99 } = \frac { 90 } { 10 }$
B) $\frac { 99 } { 90 } = \frac { 10 } { 11 }$
C) $\frac { 99 } { 90 } = \frac { 11 } { 10 }$
D) $\frac { 99 } { 11 } = \frac { 10 } { 90 }$
E) $\frac { 99 } { 10 } = \frac { 90 } { 11 }$

Question

Write the statement as a proportion.
99 people is to 90 chairs as 11 people is to 10 chairs
A) $\frac { 11 } { 99 } = \frac { 90 } { 10 }$
B) $\frac { 99 } { 90 } = \frac { 10 } { 11 }$
C) $\frac { 99 } { 90 } = \frac { 11 } { 10 }$
D) $\frac { 99 } { 11 } = \frac { 10 } { 90 }$
E) $\frac { 99 } { 10 } = \frac { 90 } { 11 }$

Quizplus · Accepted Answer

To write a proportion, we compare two equivalent ratios. The first ratio is the number of people to the number of chairs, which is 99:90. The second ratio is 11:10. To make the ratios equivalent, we need to multiply both the numerator and denominator of the second ratio by the same factor that we multiplied the first ratio to get from 99 to 11. We multiplied by 11/99, so we do the same to the second ratio:

11/99 = x/10

To solve for x, we cross-multiply:

99x = 110

x = 110/99

So the second ratio is 11: (110/99). Now we can compare the ratios:

99:90 = 11:(110/99)

To simplify the second ratio, we can multiply both the numerator and denominator by 99:

99:90 = 11x99/99:(110x99/99)

Simplifying further:

99:90 = 11:10

Write the Statement as a Proportion 1199=9010\frac { 11 } { 99 } = \frac { 90 } { 10 }9911​=1090​

Write the Statement as a Proportion $\frac { 11 } { 99 } = \frac { 90 } { 10 }$