At a certain university, the ratio of doctoral students to master’s students is
3 to 5. If there are 9,000 doctoral students, how many master’s students are
there?Step 1: Set up a proportion. Remember to label your units!
3 doctoral students
5 master’s students =9,000 doctoral students
m master’s studentsStep 2: Cross-multiply to solve for m:
doctoral studentsmaster’s students =^35 = 9,000/m
3 m = 9,000(5)
m = 3,000(5) = 15,000Representing Ratios Algebraically
Recall from the discussion of fractions that the denominator of a fraction specifies
the number of slices a pie is cut into, and the numerator represents the number of
slices of that pie. In a certain sense, ratios can be thought of in the same way.
If you are given a part:part ratio, such as “The ratio of boys to girls is 3 to 2,”
you can think of the number of boys as 3 slices of a pie and the number of girls as
2 slices of the same pie. Since you are not told the value of the slice of the pie, let x
represent the quantity of 1 slice. Thus if the ratio of boys to girls is 3 to 2, then:
boys
girls =3
2 =3 x
2 x
Representing ratios in this way is helpful in the following situations:Situation 1: When you know values for the parts of a ratio and want to
determine the whole, or vice versa.
In a certain business’s budget, the dollar amounts allocated for marketing,
product development, and administration are in the ratio 5:3:2. If the
business’s budget is $200,000, how much money is allocated for marketing?Step 1: Since you are not given a value for any of the parts, use x to represent
one part. Thus
5 x = dollars allocated for marketing
3 x = dollars allocated for product development
2 x = dollars allocated for administrationStep 2: Identify an algebraic relationship:
The $200,000 budget is split among the three segments, so the sum of the
amounts for the three segments will equal $200,000:
5 x + 3x + 2x = $200,000244 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 244 12/05/17 11:52 am