Exam 19: Ratio, Proportion, and Variation

Find two numbers that are to each other as $12: 19$ and whose difference is 49 .

Determine the values of $a, b$ , and $c$ if $a: b: c=1: 4: 9$ and $2 a+3 b-c=4$ .

Find the mean proportional between 21 and 84 .

If $y$ varies inversely as $x$ and $y$ is 94 when $x$ is 582 , find $y$ when $x$ is 116 .

The weight of a piece of sheet metal with given thickness is proportional to its area. If a sheet of copper with dimensions $2.5 \mathrm{~m} \times 3.4 \mathrm{~m}$ weighs $45 \mathrm{~kg}$ , what is the weight of a sheet of copper with the same thickness, length $5 \mathrm{~m}$ , and width $1.7 \mathrm{~m}$ ?

If $m$ is directly proportional to $n$ and $m$ is 4 when $n$ is 32 , find $m$ when $n$ is 48 .

Determine the values of $x, y, z$ , and $u$ given that $x+y+z+u=90$ and $x: y: z: u=3: 4: 5: 6$ .

Assume $y$ is directly proportional to the $3 / 2$ power of $x$ and has a value of 3.22 when $x$ is 30.9 . (a) Find the constant of proportionality. (b) Write the equation $y=\mathrm{f}(x)$ . (c) Find $y$ when $x=40.3$ . (d) Find $x$ when $y=2.79$ .

If $y$ varies directly as the square of $x$ and $y$ is 45 when $x$ is 3 , find $y$ when $x$ is 6 .

The time $t$ for the swing of a simple pendulum varies directly as the square root of the length $L$ . If the time of the swing is $1.5 \mathrm{~s}$ when the length is $8 \mathrm{~cm}$ , find the time of the swing when the length of the pendulum is $1.2 \mathrm{~cm}$ .

The scale on a map shows that $1.2 \mathrm{~cm}$ represents $155 \mathrm{~km}$ . If two cities are $365 \mathrm{~km}$ apart, how far apart will they appear on the map?

If $y$ varies directly as $x$ and $x$ is 15 when $y$ is 27 , find $x$ when $y$ is 432 .

If $y$ varies directly as the cube of $x$ and $y$ is 54 when $x$ is 3 , find $y$ when $x$ is 2.5 .

If $y$ is inversely proportional to the square of $x$ and has a value of 901 when $x$ is 211 , find $y$ when $x$ is 103 .

If $x$ is directly proportional to $y$ and $x$ is 1.28 when $y$ is 32.0 , find $x$ when $y$ is 13.1 .

Find $x$ where $9: x=13.5: 2$ .

If $y$ varies directly as the square root of $x$ and $y$ is 33.1 when $x$ is 274 , find $y$ when $x$ is 145 .

Find $x$ where $x:(8+x)=1: 5$ .

The volume of a square-based pyramid varies directly as the square of the base and the height. If the height is decreased by $15 \%$ and the base is increased by $12 \%$ , how does the volume change?

When a gas expands at a constant temperature its pressure varies inversely as its volume. If the pressure of a certain gas is $40 \mathrm{~kg} / \mathrm{m}^{2}$ when its volume is $0.8 \mathrm{~m}^{3}$ , determine the pressure when the volume of the gas is $0.1 \mathrm{~m}^{3}$ ?