When two proportional relationships are represented in different ways, we compare them by finding a common piece of information.
For example, Clare’s earnings are represented by the equation y=14.5x, where y is her earnings in dollars for working x hours.
The table shows some information about Jada’s pay.
Who is paid at a higher rate per hour? How much more does that person have after 20 hours?
|
time worked (hours) |
earnings (dollars) |
row 1 |
7 |
92.75 |
row 2 |
4.5 |
59.63 |
row 3 |
37 |
490.25 |
In Clare’s equation we see that the constant of proportionality relating her earnings to time worked is 14.50. This means that she earns $14.50 per hour.
We can calculate Jada’s constant of proportionality by dividing a value in the earnings column by a value in the same row in the time worked column. Using the last row, the constant of proportionality for Jada is 13.25, since 490.25\div37=13.25. An equation representing Jada’s earnings is y=13.25x. This means she earns $13.25 per hour.
So Clare is paid at a higher rate than Jada. Clare earns $1.25 more per hour than Jada, which means that after 20 hours of work, she has 20\boldcdot \$1.25 = \$25 more than Jada.