Answer:
1a. 42 liters
1b. 345 miles
2a. 10 h 20 min 41.4 sec
2b. 361.6 km
5a. $8
5b. 444.5 km
5c. 46 h 13 min 20.9 sec
5d. $160
Step-by-step explanation:
Each of these problems expresses a proportion and asks you to find a missing value. You are given, for example, <em>value 1</em> and <em>related value 1.</em> You are asked to find <em>value 2</em> that corresponds to <em>related value 2</em>.
<em>Solving the Proportion</em>
Expressed as a proportion, this looks like ...
... (<em>value 1</em>)/(<em>related value 1</em>) = (<em>value 2</em>)/(<em>related value 2</em>)
If you multiply both sides of this equation by <em>related value 2</em>, you can find <em>value 2</em>.
... (<em>related value 2</em>)/(<em>related value 1</em>)×(<em>value 1</em>) = <em>value 2</em>
<em>Another way to think about it</em>
I like to think of the <em>related values</em> as making a fraction. If the <em>related value 2</em> is larger than <em>related value 1</em>, the fraction is greater than 1 and the <em>value 2</em> will be larger than <em>value 1</em>. (This realization can serve as a check on your answer.)
1a. <em>related value 2</em> = 168 km. This is the value for which you want to find <em>value 2</em>, the number of liters of gasoline. <em>related value 1</em> has the same units as <em>related value 2</em> (km), and <em>value 1</em> has the same units as <em>value 2</em> (liters).
Then the fraction of interest is (168 km)/(468 km), and it multiplies 117 L. The result is ...
... (168/468)×(117 L) = 42 L
1b. (10 h)/(4 h)×(138 mi) = 345 mi
2a. (180 mi)/(261 mi)×(15 h) ≈ 10.3448 h
2b. (4 h)/(5 h)×(452 km) = 362.6 km
You may have noticed that I keep the units with the numbers. When the same units are in the numerator and denominator, they cancel—the way any common factors cancel. The remaining units will be the units of the answer. This practice of keeping units with numbers can help ensure you're using the right numbers for the right purpose. If the units don't work out, your math has an error.
5a. (2 lb)/(50 lb)×$200 = $8
5b. (7 h)/(6 h)×381 km = 444.5 km
5c. (459 km)/(427 km)×(43 h) ≈ 46.2225 h
5d. (20 kg)/(11 kg)×$88 = $160
