1.15.5 Practice

1. If y varies directly as $x$ and $y=14$, when $x=3$. Find the equation that relates $x$ and $y$.

2. The price, $P$, that Eric pays for gas varies directly with the number of gallons, $g$, he buys. It costs him $50 to buy 20 gallons of gas. Choose the equation that relates $P$ and $g$.

3. Joseph is traveling on a road trip. The distance, $d$, he travels before stopping for lunch varies directly with the speed, $v$, he travels. He can travel 120 miles at a speed of 60 mph. How many miles would he travel before stopping for lunch at a rate of 65 mph?

4. The mass of a liquid, $M$, varies directly with its volume, $V$. A liquid with mass 16 kilograms has a volume of 2 liters. What is the volume, in liters, of this liquid if its mass is 128 kilograms?

5. The length, $L$, that a spring stretches varies directly with a weight, $W$, placed at the end of the spring. When Sarah placed a 10-pound watermelon on a hanging scale, the spring stretched 5 inches. What weight of watermelon, in pounds, would stretch the spring 6 inches?

6. The maximum load a beam, $M$, will support varies directly with the square of the diagonal of the beam’s cross-section, $d^2$. A beam with diagonal 6 inch will support a maximum load of 108 pounds. What load, in pounds, will a beam with a 10-inch diagonal support?

7. The number of calories, $c$, burned varies directly with the amount of time, $t$, spent exercising. Arnold burned 312 calories in 65 minutes exercising. How many calories would he burn if he exercises for 90 minutes?