91Ó°ÊÓ

In the following exercises, solve. The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10 pound watermelon on a hanging scale, the spring stretched 5 inches. (a) Write the equation that relates the length of the spring to the weight. (b) What weight of watermelon would stretch the spring 6 inches?

In the following exercises, solve. The maximum load a beam will support varies directly with the square of the diagonal of the beam's cross-section. A beam with diagonal 6 inch will support a maximum load of 108 pounds. (a) Write the equation that relates the load to the diagonal of the cross- section. (b) What load will a beam with a 10 inch diagonal support?

In the following exercises, solve. If \(y\) varies inversely with \(x\) and \(y=5\) when \(x=4\) find the equation that relates \(x\) and \(y\).

In the following exercises, solve. If \(a\) varies inversely with \(b\) and \(a=12\) when \(b=\frac{1}{3}\) find the equation that relates \(a\) and \(b\).

The fuel consumption (mpg) of a car varies inversely with its weight. A Toyota Corolla weighs 2800 pounds and gets \(33 \mathrm{mpg}\) on the highway. (a) Write the equation that relates the mpg to the car's weight. (b) What would the fuel consumption be for a Toyota Sequoia that weighs 5500 pounds?

Write an inverse variation equation to solve the following problems. Paul, a dentist, determined that the number of cavities that develops in his patient's mouth each year varies inversely to the \(\begin{array}{lll}\text { number of } & \text { minutes } & \text { spent }\end{array}\) brushing each night. His patient, Lori, had 4 cavities when brushing her teeth 30 seconds \((0.5\) minutes) each night. (a) Write the equation that relates the number of cavities to the time spent brushing. (b) How many cavities would Paul expect Lori to have if she had brushed her teeth for 2 minutes each night?

Write an inverse variation equation to solve the following problems. The number of tickets for \(a\) sports fundraiser varies inversely to the price of each ticket. Brianna can buy 25 tickets at \(\$ 5 e a c h\). (a) Write the equation that relates the number of tickets to the price of each ticket. (b) How many tickets could Brianna buy if the price of each ticket was \(\$ 2.50 ?\)

If \(p\) varies directly as \(q\) and \(p=10,\) when \(q=2\). find the equation that relates \(p\) and \(q\).

The length a spring stretches varies directly with a weight placed at the end of the spring. When Meredith placed a 6-pound cantaloupe on a hanging scale, the spring stretched 2 inches. How far would the spring stretch if the cantaloupe weighed 9 pounds?