Chapter 3

Write the fraction in simplest form. $$ \frac{36}{48} $$

There are a total of 28 marbles in a bag. Six of the marbles are red and the rest are blue. What is the ratio of red marbles to blue marbles? A. \(\frac{2}{11}\) B. \(\frac{6}{28}\) C. \(\frac{3}{14}\) D. \(\frac{3}{11}\)

Your school's drama club charges \(\$ 4\) per person for admission to the play Our Town. The club borrowed \(\$ 400\) from parents to pay for costumes and props. After paying back the parents, the drama club has \(\$ 100 .\) How many people attended the play? Choose the equation that represents this situation and solve it. A. \(4 x+400=100\) B. \(4 x+100=400\) C. \(4 x-400=100\)

Write the sentence as an equation. Let x represent the number. Use mental math to solve the equation. Then check your solution. (Lesson 1.5).The sum of a number and 18 is 45.

Solve the equation. $$ -3(7-3 n)+2 n=5(2 n-4) $$

SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ \frac{3}{7} x=6 $$

Without writing the steps of a solution, determine whether the equation has one solution, no solution, or is an identity. $$ 6 a+8=2 a $$

Solve the equation by simplifying first. $$ 6=y-(-11) $$

Write the fraction in simplest form. $$ \frac{28}{32} $$

If you drive a car \(m\) miles in 2 hours, which expression will give the average speed of the car? F. \(m+2\) G. \(2 m\) H. \(\frac{m-2}{2}\) J. \(\frac{m}{2}\)

You have a 90-pound calf you are raising for a 4-H project. You expect the calf to gain 65 pounds per month. In how many months will the animal weigh 1000 pounds?

Write the sentence as an equation. Let x represent the number. Use mental math to solve the equation. Then check your solution. (Lesson 1.5).The product of a number and 21 is 105.

Solve the equation. $$ 4 x+3(x-2)=-5(x-4)-x $$

SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ -\frac{4}{5} x=36 $$

Without writing the steps of a solution, determine whether the equation has one solution, no solution, or is an identity. $$ 8+6 a=2 a+8 $$

Solve the equation by simplifying first. $$ x-(-8)=13 $$

Write the fraction in simplest form. $$ \frac{9}{27} $$

You travel 154 miles on half a tank of fuel. Your car gets 22 miles per gallon. How many gallons of fuel can your tank hold? A. 7 B. 14 C. 22 D. 132

The formula \(d=\frac{n}{2}+26\) relates nozzle pressure \(n\) (in pounds per square inch) and the maximum distance the water reaches \(d\) (in feet \()\) for a fire hose with a certain size nozzle. Solve for \(n\) to find how much pressure is needed to reach a fire 50 feet away.

Evaluate the expression. (Lesson 2.2) $$|9|$$

Solve the equation. $$ -7+8(5-3 q)=3(7-9 q) $$

What power of ten would you multiply the equation 5.692x 1.346 8.451x by to change it to an equivalent equation with integer coefficients? $$ (A)10^{1} $$ $$ (B)10^{2} $$ $$ (C)10^{3} $$ $$ (D)10^{4} $$

ERROR ANALYSIS Find and correct the error. $$ \frac{2}{5} x=10 $$ $$ \left(\frac{5}{2}\right)\left(\frac{2}{5} x\right)=10 $$ $$ x=10 $$

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

Solve the equation by simplifying first. $$ r-(-7)=-16 $$

You want to exchange 60 dollars Canadian dollars into United States dollars. The exchange rate is 1.466 Canadian dollars per United States dollar on the day you exchange the money. How many United States dollars will you get? F. 41 dollars G. 46 dollars H. 131 dollars J. 221 dollars

Solve the equation. \(4(2 y+1)-6 y=18\)

Evaluate the expression. (Lesson 2.2) $$|-32|$$

Solve the equation. $$ y+2(y-6)=-(2 y-14)+49 $$

ERROR ANALYSIS Find and correct the error. $$ -\frac{3}{4} x=6 $$ $$ \frac{4}{3}\left(-\frac{3}{4} x\right)=\frac{4}{3}(6) $$ $$ x=8 $$

Steamboats carried cotton and passengers up and down the Mississippi River in the mid- 1800 s. A steamboat could travel 8 miles per hour downstream from Natchez, Mississippi, to New Orleans, Louisiana, and only 3 miles per hour upstream from New Orleans to Natchez. It was about 265 miles each way. If it took a steamboat 55 more hours to go upstream than it did to go downstream, how long did it take to complete the roundtrip? Solve \(8 t=3(t+55),\) where \(t\) is the time (in hours) it takes the steamboat to travel downstream and \((t+55)\) is the time it takes to travel upstream.

Solve the equation by simplifying first. $$ 19-(-y)=25 $$

Solve the equation. \(22 x+2(3 x+5)=66\)

Evaluate the expression. (Lesson 2.2) $$-|5|$$

Solve the equation. $$ \frac{1}{3}(3 x-12)=6-2(x-1) $$

The cross-country track team ran 8.7 kilometers in 42.5 minutes during their workout. Which equation could you use to find r, the team’s average running speed (in kilometers per minute)? $$ (A)8.7 r=42.5 $$ $$ (B)42.5 r=8.7 $$ $$ (C)42.5+r=8.7 $$ $$ (D)8.7+r=42.5 $$

MODELING REAL-LIFE PROBLEMS Use the verbal model to write a linear equation. Then use the multiplication property of equality to solve the equation. It takes 45 peanuts to make one ounce of peanut butter. How many peanuts will be needed to make a 12 -ounce jar of peanut butter? \(\frac{\text { Number of peanuts }}{\text { Number of ounces }}=\) Number of peanuts per ounce

A cheetah running 90 feet per second is 100 feet behind a gazelle running 70 feet per second. How long will it take the cheetah to catch up to the gazelle? Use the verbal model to write and solve a linear equation. Speed of cheetah \( \cdot \text { Time }=100+\text { Speed of gazelle } \cdot\text { Time }\)

Solve the equation by simplifying first. $$ 2-(-b)=-6 $$

Graph the numbers on a number line.Then write two inequalities that compare the numbers. $$4,-3$$

Solve the equation. \(6 x+3(x+4)=15\)

Evaluate the expression. (Lesson 2.2) $$-|-16|$$

Solve the equation. $$ 2(6-2 x)=-9 x-\frac{1}{2}(-4 x+6) $$

MODELING REAL-LIFE PROBLEMS Use the verbal model to write a linear equation. Then use the multiplication property of equality to solve the equation. You ate 3 of the 8 slices of a pizza. You paid 3.30 dollars as your share of the total cost of the pizza. How much did the whole pizza cost? $$ \frac{\text { Number of pieces you ate }}{\text { Total number of pieces }} \cdot\left[\begin{array}{l} {\text { cost of the }} \\ {\text { whole pizza }} \end{array}\right]=\left[\begin{array}{l} {\text { Your share }} \\ {\text { of the cost }} \end{array}\right] $$

Solve the equation by simplifying first. $$ x+5-2=6 $$

Graph the numbers on a number line.Then write two inequalities that compare the numbers. $$-5,-2$$

Solve the equation. \(7-(2-g)=-4\)

Write the numbers in order from least to greatest. (Skills Review p. 770) $$1301,1103,1031,1013,1130$$

The diagram shows the orbits of Jupiter’s four largest moons: Io, Europa, Ganymede, and Callisto. The orbits are circular. Io’s orbit is x kilometers (km) from Jupiter. The distance between Io and Europa is 300,000 km. The distance between Europa and Ganymede is 400,000 km. The distance between Ganymede and Callisto is 800,000 km. The distance from Jupiter to Callisto is \(4 \frac{3}{4} x,\) or \(4 \frac{3}{4}\) times the distance from Jupiter to Io. Find the distance \(x\) between Jupiter and Io, using the equation \(x+300,000+400,000+800,000=4 \frac{3}{4} x\)

BUNDLING NEWSPAPERS You are loading a large pile of newspapers onto a truck. You divide the pile into four equal-size bundles. One bundle weighs 37 pounds. You want to know the weight \(x\) of the original pile. Which equation represents this situation? Solve the correct equation. A. \(\frac{x}{4}=37\) B. \(4 x=37\) c. \(37 x=4\)