Review Exercises

There are nine saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.

One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.

The sum of two consecutive integers is $\mathrm{-135}.$ Find the numbers.

Find three consecutive odd integers whose sum is 51.

What number is 67% of 250?

What percent of 125 is 150?

Dolores bought a crib on sale for $350. The sale price was 40% of the original price. What was the original price of the crib?

Angel received a raise in his annual salary from $55,400 to $56,785. Find the percent change.

Emmett bought a pair of shoes on sale at 40% off from an original price of $138. Find ⓐ the amount of discount and ⓑ the sale price.

Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350% mark-up. Find ⓐ the amount of the mark-up and ⓑ the list price.

Moira borrowed $4,500 from her grandfather to pay for her first year of college. Three years later, she repaid the $4,500 plus $243 interest. What was the rate of interest?

Solve the formula
$V=LWH$ for L.

Solve the formula
$h=48t+\frac{1}{2}a{t}^2$ for a.

What is the height of a triangle with area $67.5$ square meters and base 9 meters?

The perimeter of a triangle is 97 feet. One side of the triangle is eleven feet more than the smallest side. The third side is six feet more than twice the smallest side. Find the lengths of all sides.

Find the length of the missing side. Round to the nearest tenth, if necessary.

Seong is building shelving in his garage. The shelves are 36 inches wide and 15 inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

The width of a rectangle is three more than twice the length. The perimeter is 96 inches. Find the length and the width.

Paulette has $140 in $5 and $10 bills. The number of $10 bills is one less than twice the number of $5 bills. How many of each does she have?

Tickets for a basketball game cost $2 for students and $5 for adults. The number of students was three less than 10 times the number of adults. The total amount of money from ticket sales was $619. How many of each ticket were sold?

Yumi spent $34.15 buying stamps. The number of $0.56 stamps she bought was 10 less than four times the number of $0.41 stamps. How many of each did she buy?

Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tile. She will use basic tiles that cost $8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?

When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa two hours to drive the same distance. Elsa’s speed is seven miles per hour faster than Gabe’s speed. Find Gabe’s speed and Elsa’s speed.

Two busses leave Amarillo at the same time. The Albuquerque bus heads west on the I-40 at a speed of 72 miles per hour, and the Oklahoma City bus heads east on the I-40 at a speed of 78 miles per hour. How many hours will it take them to be 375 miles apart?

At 6:30, Devon left her house and rode her bike on the flat road until 7:30. Then she started riding uphill and rode until 8:00. She rode a total of 15 miles. Her speed on the flat road was three miles per hour faster than her speed going uphill. Find Devon’s speed on the flat road and riding uphill.

$x<\text{−}1$

$x\le \frac{5}{4}$

$\mathrm{-2}<x<0$

$0\le x\le 3.5$

$a+\frac{2}{3}\ge \frac{7}{12}$

$\frac{q}{\mathrm{-2}}\ge \mathrm{-24}$

$9h-7(h-1)\le 4h-23$

$\frac{3}{8}a-\frac{1}{12}a>\frac{5}{12}a+\frac{3}{4}$

Three less than c is at least 360.

Negative two times a is no more than eight.

Rogelio paints watercolors. He got a $100 gift card to the art supply store and wants to use it to buy 12″ × 16″ canvases. Each canvas costs $10.99. What is the maximum number of canvases he can buy with his gift card?

Renee’s car costs her $195 per month plus $0.09 per mile. How many miles can Renee drive so that her monthly car expenses are no more than $250?

Jenna is planning a five-day resort vacation with three of her friends. It will cost her $279 for airfare, $300 for food and entertainment, and $65 per day for her share of the hotel. She has $550 saved towards her vacation and can earn $25 per hour as an assistant in her uncle’s photography studio. How many hours must she work in order to have enough money for her vacation?

$4x-2\le 4$ and
$7x-1>\text{−}8$

$\frac{3}{4}\left(x-8\right)\le 3$ and
$\frac{1}{5}\left(x-5\right)\le 3$

$\mathrm{-5}\le 4x-1<7$

$3\left(2x-3\right)<\text{−}5$ or
$4x-1>3$

$2\left(x+3\right)\ge 0$ or
$3\left(x+4\right)\le 6$

Liam is playing a number game with his sister Audry. Liam is thinking of a number and wants Audry to guess it. Five more than three times her number is between 2 and 32. Write a compound inequality that shows the range of numbers that Liam might be thinking of.

$\left|x\right|=8$

$\left|z\right|=0$

$4\left|x-1\right|+2=10$

$\left|\frac{1}{2}x+5\right|+4=1$

$\left|x\right|\le 8$

$\left|6x-5\right|<7$

$\left|x\right|>6$

$\left|x-5\right|>\text{−}2$

$3\left|x\right|+4\ge 1$

At Fancy Grocery, the ideal weight of a loaf of bread is 16 ounces. By law, the actual weight can vary from the ideal by 1.5 ounces. What range of weight will be acceptable to the inspector without causing the bakery being fined?