Let’s use equations to solve problems involving proportional relationships.
Without calculating, order the quotients of these expressions from least to greatest.
$42.6 \div 0.07$
$42.6 \div 70$
$42.6 \div 0.7$
$426 \div 70$
Place the decimal point in the appropriate location in the quotient: $42.6 \div 7 = 608571$
Use this answer to find the quotient of one of the previous expressions.
A performer expects to sell 5,000 tickets for an upcoming concert. They want to make a total of \$311,000 in sales from these tickets.
Aluminum cans can be recycled instead of being thrown in the garbage. The weight of 10 aluminum cans is 0.16 kilograms. The aluminum in 10 cans that are recycled has a value of \$0.14.
The EPA estimated that in 2013, the average amount of garbage produced in the United States was 4.4 pounds per person per day. At that rate, how long would it take your family to produce a ton of garbage? (A ton is 2,000 pounds.)
Remember that if there is a proportional relationship between two quantities, their relationship can be represented by an equation of the form $y = k x$. Sometimes writing an equation is the easiest way to solve a problem.
For example, we know that Denali, the highest mountain peak in North America, is 20,300 feet above sea level. How many miles is that? There are 5,280 feet in 1 mile. This relationship can be represented by the equation
$$f=5,\!280 m$$
where $f$ represents a distance measured in feet and $m$ represents the same distance measured miles. Since we know Denali is 20,310 feet above sea level, we can write
$$20,\!310=5,\!280 m$$
So $m = \frac{20,310}{5,280}$, which is approximately 3.85 miles.
