Quiz about Equation and Inequalities

Question 1

Mrs. Dawson's twenty-five member dance class is raising funds to participate in a local dance competition. They plan to raise at least $1300 to cover the cost of entry fees. The class has currently raised $550.

If each dance member raises an equal amount of money, which of the following can be used to determine, a, the amount of money each team member could raise to meet the goal?

Accepted Answer

$$550+25a\ge1300$$

Answer

$$\frac{1300}{25a}\ge550$$

Answer

$$25a+550\le1300$$

Answer

$$550a+25>1300$$

Question 2

A new office building is opening downtown. The largest office space available to rent is 2000 square feet. A company with 6 employees rents space in the building. Each employee will have an equivalent amount of office space, and there will be a 350 square foot lounge space.

Which of the following can be used to determine, s, the number of square feet of office space each employee could receive?

Accepted Answer

$$6s+350=2000$$

Answer

$$2000\ge350+6s$$

Answer

$$2000\le350-6s$$

Answer

$$2000\ge350-6s$$

Question 3

Which situation is best described by the equation below?

$$5x-12=32$$

Accepted Answer

The temperature begins at 12 degrees below zero and rises five degrees each hour to reach thirty-two degrees. How many hours did it take the temperature to reach thirty-two degrees?

Answer

The temperature begins at 12 degrees below zero and falls five degrees each hour to reach thirty-two degrees. How many hours did it take the temperature to reach thirty-two degrees?

Answer

The temperature begins at 5 degrees and falls 12 degrees each hour to reach thirty-two degrees. How many hours did it take the temperature to reach thirty-two degrees?

Answer

The temperature begins at 5 degrees and rises 12 degrees each hour to reach thirty-two degrees. How many hours did it take the temperature to reach thirty-two degrees?

Question 4

Look at the inequality shown below.

$$9.25x-120\ge85$$

Which situation best matches the inequality?

Accepted Answer

Malina earns $9.25 per hour babysitting. She needs a minimum of $85 to attend a concert. If she spends $120 on clothes at the mall, how many hours must Malina work to be able to afford the concert?

Answer

Malina earns $9.25 per hour babysitting. She needs $85 to attend a concert. If she spends at most $120 on clothes at the mall, how many hours must Malina work to be able to afford the concert?

Answer

Malina babysits for 9.25 hours. She needs a maximum of $85 to attend a concert. If she spends $120 on clothes at the mall, how much money must Malina earn per hour to be able to afford the concert?

Answer

Malina babysits 9.25 hours. She needs more than $85 to attend a concert. If she spends $120 on clothes at the mall, how much money must Malina earn per hour to be able to afford the concert?

Question 5

Avery need a total of $12.75 in quarters at the laundromat. She has already saved $3.25. Which equation and solution process can be use to determine, q, the number of additional quarters Avery needs to wash her laundry?

Accepted Answer

$$12.75=0.25q+3.25$$
Subtract 3.25 from both sides and divide the difference by 0.25.

Answer

$$12.75=\frac{q}{25}+3.25$$
Subtract 3.25 from both sides and multiply the difference by 25.

Answer

$$3.25-0.25q=12.75$$
Subtract 3.25 from both sides and divide the difference by -0.25.

Answer

$$25q+3.25=12.75$$
Subtract 3.25 from both sides and divide the difference by 25.

Question 6

Which best represents the inequality and solution to the sentence below?

The quotient of a number and -4 decreased by 5 is at most 15.

Accepted Answer

$$\frac{x}{-4}-5\le15;\ x\ge-80$$

Answer

$$-5+\frac{x}{4}\le15;\ x\le80$$

Answer

$$\frac{x}{4}-5>15;\ x>80$$

Answer

$$\frac{x}{-4}-5<15;\ x>80$$

Question 7

Serenity is four years younger than twice her brother's age. Serenity is 18 years old. Which model and solution best represents, x, the age of Serenity's brother?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 8

The weight limit for luggage on Mavis' vacation flight is 50 pounds. Her suitcase currently weighs 42 pounds, and she has 3 more pairs of shoes to pack. She uses the inequality $$50\ge42+3s$$ where s is the weight per pair of shoes. Which of the following could NOT represent the weight of each pair of shoes?

Accepted Answer

Answer

Answer

Answer

Question 9

Ross purchases an electric guitar. He has $225 to put towards the purchase. He saves $50 each month until he has enough money for the guitar. The equation below shows the relationship between the number of months Ross must save and the cost of the electric guitar.

$$425=225+50m$$

Which of the following best represents the number of months Ross needs to save in order to purchase the guitar?

Accepted Answer

<html><head></head><body>4 months</body></html>

Answer

12.5 months

Answer

<html><head></head><body>10 months</body></html>

Answer

<html><head></head><body>4.5 months</body></html>

Question 10

Alfonso reads a 356- page book for English class. He reads twenty-five pages a day and finished reading thirty-four pages so far. If $$25d+31=356$$ can be used to determine the number of days Alfonso needs to complete the book, which of the following is the solution to the equation?

Accepted Answer

Answer

Answer

Answer

Question 11

Faye is 14 years old. Her age is 3 years less than half the age of Betsy. The equation below can be used to determine Betsy's age.

$$\frac{x}{2}-3=14$$

Which value represents Betsy's age?

Accepted Answer

Answer

Answer

Answer

Question 12

Question 12.

Accepted Answer

$$3x+75=90;\ x=5$$

Accepted Answer

$$3x+75+90=180;\ x=5$$

Answer

$$3x=75;\ x=25$$

Answer

$$3x+75+90=360;\ x=65$$

Question 13

Which of the following equations CANNOT be used to determine the value of x?

Accepted Answer

$$180+28.4=x+x$$

Answer

$$x+x+28.4=180$$

Answer

$$180-28.4=2x$$

Answer

$$28.4+2x=180$$

Question 14

Angle H and angle J are complementary angles. The measure of angle H is five times the measure of angle J. Which shows an equation and solution for the measure of angle J?