RATIO/PROPORTION WORD PROBLEMS
A ratio/rate is the comparison of two quantities.
Examples:
The ratio of 12 miles to 18 miles = 12 mi / 18 mi = 2 mi / 3 mi.
The rate of $22.50 for 3 hours = $22.50 / 3 hrs
NOTE:
1) Ratios and rates are written as a proper or improper fraction. They are not left as a mixed number.
2) Ratios and rates are reduced to lowest terms.
When you are asked to simplify ratios/rates, you are to convert to like units (when possible) and reduce.
EXAMPLES:
1) Simplify the ratio of 1.5 feet to 4 inches
convert 1.5 ft to inches (12 inches = 1 foot)
1.5 ∙ 12 = 18 inches
1.5 ft = 18 in = 9
4 in 4 in 2
2) Simplify $646 for 40 hours to a unit rate.
A unit rate is how much money for one hour.
$646 = 646 ÷ 40 = 16.15
40 hrs
The unit rate is $16.15 per hour or $16.15/hour.
A proportion is two ratios/rates set equal to each other. Proportions are useful when solving word problems with ratios or rates as the given information.
When setting up a proportion, keep in mind: Same line, same information.
For example, if one ratio is set up as money to hours, then the other ratio should be set up as money to hours.
EXAMPLES:
1) A recipe calls for 2 eggs for every 5 cups of flour. A local chef will use 35 cups of flour, how many eggs must he have?
The given ratio is 2 eggs/ 5 cups.
equation: 2 eggs = x eggs
5 cups 35 cups
solve: 2(35) = 5x
14 = x
The chef will need 14 eggs.
2) If a watch is losing 1.5 minutes for every 12 hours that go by, how many minutes will it lose in one week?
The given ratio is 1.5 minutes / 12 hours.
equation: 1.5 minutes = x minutes
12 hours 1 week
Note: We need to convert 1 week to hours because the units must be the same.
use: 24 hours = 1 day, 7 days = 1 week,
therefore: 1 week = 168 hours (24∙ 7)
equation: 1.5 minutes = x minutes
12 hours 168 hours
solve: 1.5(168) = 12x
21 = x
The watch will lose 21 minutes in one week.
3) Five out of every seven households have cable TV. If 42,000 households in a certain city have a TV, how many do not have cable TV?
The given ratio is 5 cable TV/ 7 households.
equation: 5 cable TV = x cable TV
7 household 42000 household
solve: 5(42000) = 7x
30000 = x
In the proportion the variable represents how many have cable TV. However, the question asks how many do not have cable TV. Do not assume that once you solve the equation you have answered the question.
Total household with TV - have cable = do not have cable
42000 - 30000 = 12000
Out of the 42,000 households that have a TV, 12000 do not have cable TV.