Chapter 3

In Exercises \(32-37\), convert the units. Round the result to the nearest tenth. 2000 meters to kilometers (1 kilometer \(=1000\) meters)

Write the steps you would use to solve the equation \(3(x-4)+2 x=6-x .\) Beside each step, write an explanation of the step. Then show how to check your answer.

To raise money, your student council is selling magazine subscriptions. The student council will receive a one-time bonus of $150 from the magazine publisher plus 38% of the subscription money. The following verbal model represents the situation. Write a linear equation from the verbal model. HINT: Remember to write the percent in decimal form: 38% 0.38.

SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ \frac{3}{4} k=1 $$

Solve the equation if possible. Determine whether the equation has one solution, no solution, or is an identity. $$ 8 c-4=20-4 c $$

Solve the equation. $$ t-5=-20 $$

Solve the equation. \(\frac{1}{4}(t+10)=5\)

You ride a stationary bike at the gym. After your last five visits you wrote down how long you rode the bike and how many miles you pedaled, What yous your average speed in miles per minute? $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Number of miles } & {9} & {10} & {12} & {15} & {18} \\ \hline \text { Number of minutes } & {30} & {30} & {35} & {45} & {45} \\ \hline \end{array} $$

To raise money, your student council is selling magazine subscriptions. The student council will receive a one-time bonus of 150 dollar from the magazine publisher plus 38% of the subscription money. The following verbal model represents the situation. How much subscription money is needed for the council to raise a total of $300? Round your answer to the nearest dollar.

SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ -\frac{2}{5} y=4 $$

Solve the equation if possible. Determine whether the equation has one solution, no solution, or is an identity. $$ 24-6 r=6(4-r) $$

Solve the equation. $$ x+7=-14 $$

Write the fraction in simplest form. $$ \frac{21}{49} $$

Solve the equation. \(\frac{2}{3}(x+3)=6\)

Solve \(4.5-7.2 x=3.4 x-49.5 .\) Round to the nearest tenth. You can multiply an equation with decimal coefficients by a power of ten to get an equivalent equation with integer coefficients. Multiply each side of this equation by 10 to rewrite the equation without decimals. $$ \begin{aligned} 4.5-7.2 x &=3.4 x-49.5 \\ 10(4.5-7.2 x) &=10(3.4 x-49.5) \\ 45-72 x &=34 x-495 \\ 45 &=106 x-495 \\ 540 &=106 x \\ \frac{540}{106} &=x \\ 5.094339623 & \approx x \\ 5.1 & \approx x \end{aligned} $$ The solution is approximately 5.1. Check this in the original equation. Solve the equation. Round to the nearest tenth. $$ 2.5 x+0.7=4.6-1.3 x $$

SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ 0=\frac{7}{8} x $$

Solve the equation if possible. Determine whether the equation has one solution, no solution, or is an identity. $$ -7+4 m=6 m-5 $$

Solve the equation. $$ 34+x=10 $$

Write the fraction in simplest form. $$ \frac{50}{85} $$

Find and correct the error. \(2(x-3)=5\) \(2 x-3=5\) \(2 x=8\) \(x=4\)

In Exercises 40 and 41 , use the following information from page \(129 .\) A bald eagle can fly at a rate of 30 miles per hour. Use unit analysis to find a bald eagle's flying rate in miles per minute.

Use \(a=\frac{p}{100} b\). Complete the sentence: When the percent p is a number greater than 100, the value of a is ____ ? than the value of the base number b.

A local computer center charges nonmembers \(\$5\) per session to use the media center. Members are charged a one-time fee of \(\$20\) and \(\$3\) per session. Use the verbal model to write an equation that can help you decide whether to become a member. Solve the equation and explain your solution.

Solve \(4.5-7.2 x=3.4 x-49.5 .\) Round to the nearest tenth. You can multiply an equation with decimal coefficients by a power of ten to get an equivalent equation with integer coefficients. Multiply each side of this equation by 10 to rewrite the equation without decimals. $$ \begin{aligned} 4.5-7.2 x &=3.4 x-49.5 \\ 10(4.5-7.2 x) &=10(3.4 x-49.5) \\ 45-72 x &=34 x-495 \\ 45 &=106 x-495 \\ 540 &=106 x \\ \frac{540}{106} &=x \\ 5.094339623 & \approx x \\ 5.1 & \approx x \end{aligned} $$ The solution is approximately 5.1. Check this in the original equation. Solve the equation. Round to the nearest tenth. $$ 1.1 x+3.2=0.2 x-1.4 $$

SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ 12=\frac{2}{3} x $$

Solve the equation if possible. Determine whether the equation has one solution, no solution, or is an identity. $$ 6 m-5=7 m+7-m $$

Solve the equation. $$ \frac{1}{3}+x=\frac{2}{3} $$

Write the fraction in simplest form. $$ \frac{16}{72} $$

Find and correct the error. \(5-3 x=10\) \(3 x=10\) \(x=5\)

Use \(a=\frac{p}{100} b\). Complete the sentence: Write a percent equation for the statement “a is 300 percent of b.” Then choose one set of values for a, b, and p that make the equation true.

You want to paint a piece of pottery. The total price is the cost of the piece plus an hourly painting rate. Studio A sells a vase for \(\$12\) and lets you paint for \(\$7\) an hour. Studio B sells a similar vase for \(\$15\) and lets you paint for \(\$4\) an hour. Which equation would you use to compare the total price at each studio? A. \(7 x-12=4 x-15\) B. \(12+7 x=15+4 x\)

Solve \(4.5-7.2 x=3.4 x-49.5 .\) Round to the nearest tenth. You can multiply an equation with decimal coefficients by a power of ten to get an equivalent equation with integer coefficients. Multiply each side of this equation by 10 to rewrite the equation without decimals. $$ \begin{aligned} 4.5-7.2 x &=3.4 x-49.5 \\ 10(4.5-7.2 x) &=10(3.4 x-49.5) \\ 45-72 x &=34 x-495 \\ 45 &=106 x-495 \\ 540 &=106 x \\ \frac{540}{106} &=x \\ 5.094339623 & \approx x \\ 5.1 & \approx x \end{aligned} $$ The solution is approximately 5.1. Check this in the original equation. Solve the equation. Round to the nearest tenth. $$ 3.35 x+2.29=8.61 $$

SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ 10=\frac{5}{6} x $$

Solve the equation if possible. Determine whether the equation has one solution, no solution, or is an identity. $$ 3 x-7=2 x+8+4 x $$

Solve the equation. $$ \frac{2}{5}=a-\frac{1}{5} $$

Write the fraction in simplest form. $$ \frac{48}{64} $$

Find and correct the error. \(\frac{1}{4}(x-2)=8\) \(x+2=2\) \(x=4\)

Choose the equation you would use to find 25% of 120. $$\text { (A) } 0.25 x=20$$ $$\text { (B) } x=\frac{120}{0.25}$$ $$\text { (C) } x=\frac{0.25}{120}$$ $$(D) x=(0.25)(120)$$

Solve \(4.5-7.2 x=3.4 x-49.5 .\) Round to the nearest tenth. You can multiply an equation with decimal coefficients by a power of ten to get an equivalent equation with integer coefficients. Multiply each side of this equation by 10 to rewrite the equation without decimals. $$ \begin{aligned} 4.5-7.2 x &=3.4 x-49.5 \\ 10(4.5-7.2 x) &=10(3.4 x-49.5) \\ 45-72 x &=34 x-495 \\ 45 &=106 x-495 \\ 540 &=106 x \\ \frac{540}{106} &=x \\ 5.094339623 &=x \\ 5.1 & \approx x \end{aligned} $$ The solution is approximately 5.1. Check this in the original equation. Solve the equation. Round to the nearest tenth. $$ 0.625 y-0.184=2.506 y $$

SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ \frac{5}{8} m=-20 $$

Solve the equation if possible. Determine whether the equation has one solution, no solution, or is an identity. $$ 6+3 c=-c-6 $$

Solve the equation. $$ r+\frac{3}{4}=\frac{1}{4} $$

Write the fraction in simplest form. $$ \frac{16}{32} $$

Copy the solution steps shown. Then write an explanation for each step in the right-hand column. Solution Step \(\frac{5 x}{2}+3=6\) \(\frac{5 x}{2}=3\) \(5 x=6\) \(x=\frac{6}{5}\)

In Exercises 42 and \(43,\) use 9.242 pesos per dollar as the rate of currency exchange. You are visiting Mexico and have taken \(\$ 325\) United States dollars to spend on your trip. Round to the nearest whole number. You have 840 pesos left after your trip. How many dollars will you get back?

A rock-climbing gym charges nonmembers \(16 per day to use the gym and \)8 per day for equipment rental. Members pay a yearly fee of \(450 for unlimited climbing and \)6 per day for equipment rental. Which equation represents this situation? Solve the equation to find how many times you must use the gym to justify becoming a member. A. \((16+8) x=450-6 x \quad\) B. \(24 x=450-6 x\) C. \((16+8) x=450+6 x\) D. \(16 x+8=450+6 x\)

In Exercises 43–45, use the following information. School buses that have 71 seats will be used to transport 162 students and 30 adults. Write an equation to find the number of buses needed.

SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ 12=\frac{2}{3} x $$

Without writing the steps of a solution, determine whether the equation has one solution, no solution, or is an identity. $$ 8+6 a=6 a-1 $$

Solve the equation by simplifying first. $$ t-(-4)=4 $$