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Algebra II : Proportionalities

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Example Question #12 : How To Find Inverse Variation

The number of days to construct a house varies inversely with the number of people constructing that house. If it takes 28 days to construct a house with 6 people helping out, how long will it take if 20 people are helping out?

Possible Answers:

$12.1\ days$

$8.9\ days$

$8.4\ days$

$10\ days$

$7.5\ days$

Correct answer:

$8.4\ days$

Explanation:

The statement, 'The number of days to construct a house varies inversely with the number of people constructing that house' has the mathematical relationship $D=\frac{k}{P}$ , where D is the number of days, P is the number of people, and k is the variation constant. Given that the house can be completed in 28 days with 6 people, the k-value is calculated.

$28=\frac{k}{6}$

k=28(6)=168

This k-value can be used to find out how many days it takes to construct a house with 20 people (P = 20).

$D=\frac{168}{P}$

$D=\frac{168}{20}$

D=8.4

So it will take 8.4 days to build a house with 20 people.

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Example Question #31 : Other Mathematical Relationships

The speed of a turtle is indirectly proportional to its weight in pounds. At 10 pounds, the turtle's speed was 0.5. What is the speed of the turtle if it grew and weigh 50 pounds?

Possible Answers:

0.15

0.25

0.1

0.025

0.01

Correct answer:

0.1

Explanation:

Write the formula for the indirect proportional relationship. If one variable increases, the other variable must also decrease.

xy=k

Using speed and weight as and respectively, the equation becomes:

sw=k

Use the initial condition of the turtle's speed and weight to solve for the constant.

(0.5)(10)=k

k=5

Substitute this value back into the formula. The formula becomes:

sw=5

We want to know the speed of the turtle when it is 50 pounds. Divide the variable on both sides to isolate the speed variable.

$s=\frac{5}{w}$

Substitute the new weight of the turtle.

$s=\frac{5}{50} = \frac{1}{10} = 0.1$

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Example Question #21 : Indirect Proportionality

x varies inversely with y. When x=10, y=6. When x=3, what is y?

Possible Answers:

1.8

Correct answer:

Explanation:

Inverse variation takes the form:

$y=\frac{k}{x}$

Plugging in:

$6=\frac{k}{10}$

k=60

Then solve when x=3:

3y=60

y=20

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Example Question #22 : Indirect Proportionality

The rate of speed is indirectly proportional to the time it takes to travel somewhere. If a person walks at a rate of 3 miles per hour and it takes them 4 hours to get to their destination how far did they travel?

Possible Answers:

Correct answer:

Explanation:

For an indirect proportionality, use the equation $y=\frac{k}{x}$

If rate of speed is indirectly proportional to the time, then the speed is y (3 miles per hour) and the time is x (4 hours).

Replace those into the indirect proportionality formula

$3=\frac{k}{4}$

Solve for k by multiplying by 4 on both sides

k=12

The person traveled 12 miles.

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Example Question #23 : Indirect Proportionality

A turtle moves at a pace that is inversely proportional to its weight. Suppose at five pounds it moves two feet per minute. What would be the turtle's speed in feet per minute if it weighed eight pounds?

Possible Answers:

$\frac{5}{4}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{7}{4}$

$\frac{3}{2}$

Correct answer:

$\frac{5}{4}$

Explanation:

Write the relationship for inverse proportionality. If one variable increases, the other variable must decrease.

xy=k or $y=\frac{k}{x}$

Let be the turtle's speed, and is the weight of the turtle since the turtle's speed depends on its weight.

Solve for by substituting the initial conditions.

$5=\frac{k}{2}$

Multiply by two on both sides.

k=10

Substitute this value back into the original equation.

The relationship is: $y=\frac{10}{x}$

Substitute eight pounds to find its speed.

$y=\frac{10}{8} = \frac{5}{4}$

The turtle will move at a rate of $\frac{5}{4}$ feet per minute.

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Algebra II : Proportionalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #12 : How To Find Inverse Variation

Example Question #31 : Other Mathematical Relationships

Example Question #21 : Indirect Proportionality

Example Question #22 : Indirect Proportionality

Example Question #23 : Indirect Proportionality

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