CPM Homework Help : APCALC Problem 6-11

PROPORTIONAL RELATIONSHIPS

In parts (a) through (d) below, decide whether the two given quantities are proportional. If they are, write an equation relating them and state the constant of proportionality, $k$ . If they are not proportional, explain why not.

Example: Distance $d$ traveled (in miles) when driving for $t$ hours at $a$ constant speed of $50$ mph

Solution: $d = 50t$ , $k = 50$

Cost $c$ in dollars of $n$ chocolate bars sold for $50$ cents each.
Answer (a):
$c$ and $n$ are proportional
$c = 0.50n$

Number of hours $t$ that it takes to drive $50$ miles at $r$ miles per hour.
Hint (b):
$\text{distance} = \left(\text{rate}\right)\left(\text{time}\right)$
Is rate proportional to time?

Taxi fare $f$ for $m$ miles driven. The fare is $$2$ for the first mile, then $$1$ for each subsequent mile.
Hint (c):
Write an equation for the total taxi fare.
Is this a proportional relationship?

Time $t$ it takes to read $n$ mysteries if each book takes $10$ hours to read.
Answer (d):
$t = 10n$
Is this a proportional relationship?