Multistep Proportion
Problems |
There are multiple worksheets that cover decimals. When you complete this one, be sure to move on to the next. |

For some proportion problems on the high school equivalency test, one of the numbers
to include in the ratios may not be given. However, you will be able to find
this number by adding or subtracting the numbers that **are** given.

**Example: **Carl got 2 problems
wrong for every 5 problems right on a math test. How many problems did Carl
get wrong if there were 35 problems altogether on the test?

Let’s try to set up the proportion the normal way.

__2__ (wrong) = __x__
(wrong)

5 (right) 35 (total)

Notice that our labels do not match like they did on all of the other proportion
problems. ** Wrong **matches

Since the questions asks us to the wrong items compared to the total, we ** must
**leave that ratio the way it is. Working backwards from

7 (total) 35 (total)

Now everything matches and we can solve the proportion.

2 * 35 = 70
70 ÷ 7 = 10

If Carl misses 2 out of every 7 items, on a 35 question test, he would miss
10.

**Let’s try another example.**

The ratio of men to women working at Central Hospital is 2: 9. Thirty men work at
the hospital. In all how many people work there?

** Step 1: **Set up the proportion the regular way.

9(women) = x (total)

** Step2: **Find out which part doesn't match and
then figure out how to get it to match the problem.

Men

Now let’s solve the proportion with the new numbers.

__2__ = __30__ 30 * 11 = 330 330 ÷ 2 =
165

11 x

So there are 165 people who work at the hospital.

**Let’s try one more.**

For every $10 Helen takes home, her employer withholds $3 for taxes and social
security. Helen’s gross pay each month is $1950. How much does she take home
each month?

* Step 1: *Set up the proportion as you normally
would.

3 (withheld) = 1950 (gross pay)

Notice that the top labels are the same—**take home
**The problem is that the bottom labels

** Step 2: **Let’s rewrite the proportion.

How can we change the withholding number so that it reflects gross pay?

**That’s right!** By adding the take home pay (10) and the withheld amount
(3), we get the gross pay.

__10__ (take home)
= __x__ (take home)

13 (gross pay) 1950
(gross pay)

Let’s solve the proportion now:

1. Cross multiply 1950 x 10 = 19,500

2. Divide by the remaining number 19,500 ÷ 13 = $1,500

**Helen takes home $1,500 each month.**

**Now you practice**

1. The ratio of the number of men
to the number of women working at Forms, Inc. is 7:2. Altogether there are
360 workers at the company. How many of the workers are women.

Answer

2. Recently 300 people in Central County took a civil service exam. For every
5 people who passed the exam, one person failed. How many people passed?

Answer

3. For every $9 that Fumiko makes she spends $7. The rest goes into her savings
account. If her weekly take-home pay is $540, how much does she save each week?

Answer

4. The ratio of domestic cars to imported cars in the lot at Al’s Auto Shop
is 3 : 2. There are 42 domestic cars in the shop. How many cars are there
altogether?

Answer

5. In a recent interview in Greensport, 7 out of 10 people said they prefer
coffee in the morning. The rest said that they prefer tea. 27 people said
they prefer tea. How many people were interviewed?

Answer

*Answers:
*

1.

9 360

2. **250** 5 + 1 = 6 __5__ = __p__
300 * 5 = 1500 ÷ 6 = 250 (back
to questions)

6 300

3. $120 9 – 7 = 2 __2__ = __s__
540 * 2 = 1080 ÷ 9 = 120 (back
to questions)

9 540

4. **70** 3 + 2 = 5 __3__ = __42__
42 * 5 = 210 ÷ 3 = 70 (back
to questions)

5 x

5. ** 90 ** 10 – 7= 3 __3__ = __27__
27 * 10 = 270 ÷ 3 = 90 (back
to questions)

10 x

**Resources:**

__GED Test 5: Mathematics__. (2001). Contemporary Books, NTC/Contemporary
Publishing Group: Lincolnwood, IL.

Howett, Jerry. (1998). __GED Program: Mathematics__. Cambridge
Adult Education: Upper Saddle River, NJ.

__Pre-GED: Mathematics__. (2000). Steck-Vaughn: Austin, TX.