Exam 19: Ratio, Proportion, and Variation

If $y$ varies jointly as $w$ and $x$ , and $y$ is 861 when $x$ is 20.1 and $w$ is 52.6 , find $y$ when $x$ is 66.3 and $w$ is 27.8 .

Assume $y$ is inversely proportional to the cube of $x$ and has a value of 3.25 when $x$ is 5.50 . (a) Find the constant of proportionality. (b) Write the equation $y=\mathrm{f}(x)$ . (c) Find $y$ when $x=10.2$ . (d) Find $x$ when $y=6.125$ .

Determine the values for $a$ and $b$ given that $2: a: 3=8: 16: b$ .

When a certain quantity of gas is compressed to a volume of $0.82 \mathrm{~m}^{3}$ , it has a pressure of $76 \mathrm{~Pa}$ . Find the pressure of the gas when it is compressed to $0.55 \mathrm{~m}^{3}$ . (Assume a constant temperature.)

If $y$ is inversely proportional to $x$ and has a value of 6.8 when $x$ is 3.2 , find $y$ when $x$ is 20 .

Find the value of $x: x: 10=(x+8): 18$

Determine the values for $a$ and $b$ given that $6: 7: a=b: 21: 24$ .

Find the mean proportional between 2 and 32 .

If 25000 parts are produced in 5.25 hours by five machines, find the number of parts produced by one machine in the same time?

Find the missing quantity: $\frac{4 x}{x-1}: \frac{4}{\text { ? }}$

If the pressure on a certain amount of gas is doubled, by what factor does the temperature have to change to maintain the gas at the same volume?

If $y$ varies jointly as $w$ and $x$ , and $y$ is 1.10 when $x$ is 10.1 and $w$ is 2.50 , find $x$ when $y$ is 7.50 and $w$ is 20.0 .

A car uses $7.1 \mathrm{~L}$ of fuel to travel go $10 \overline{0} \mathrm{~km}$ . How much fuel will it use to travel $364 \mathrm{~km}$ ?

If $y$ varies directly as the square of $w$ and inversely as the cube root of $x$ , by what factor will $y$ change if $w$ is halved and $x$ is tripled?

If it costs $\$ 156$ to put a fence around a square field, how much will it cost to put a fence around another square field having three times the area?

If a certain machine can produce 36000 units in 2.7 hours, how many hours will it take three of the same type machines to produce the same number of units?

Find the missing quantity: $\frac{3 x}{?}: \frac{2.4 x}{0.5}$

A certain window admits 10 watts of sunlight. By how much should every dimension of the window be increased to make the window admit 22 watts of sunlight?

If $y$ varies directly as $x$ and $y$ is 42 when $x$ is 36 , find $y$ when $x$ is 54 .

If $y$ is directly proportional to the cube of $x$ and has a value of 222 when $x$ is 9.33 , find $y$ when $x$ is 18.6 .