Deck 2: Section 2: Linear Equations and Inequalities in One Variable

Question 1

Find three consecutive integers whose sum is 216.

Answer 1

71, 72, 73

Question 2

Liam invested some money in the Abernathy Fund and $2,498 more than that amount in the Carlson Fund. For the year he was in these funds, the Abernathy fund paid 6% simple interest and the Carlson Fund paid 14% simple interest. If the income from the two funds totalled $2,250.12, then how much was invested in each fund?

Answer 2

$9,502 in Abernathy and $12,000 in Carlson

Question 3

Carol drove for 3 hours on a two-lane state road. She then increased her speed by 20 miles per hour on the freeway and drove for 5 more hours. If the total trip was 420 miles, then what was her speed on the freeway?

Answer 3

60 mph

Question 4

Mark and Brenda wish to get $135,240 for their home. The real estate agent's commission is 8% of the selling price. What should the selling price be?

Question 5

Solve.

Question 6

Translate into an algebraic expression.
35 decreased by the quotient of x and 10

Question 7

Cab drivers in Metro City charge $5 per mile plus a fixed charge of $2 for the tip. If a tourist pays $37 for a cab ride, then how many miles was the cab ride?

Question 8

Solve for x.
4(x - a) - (26b - x) = a - b

Question 9

Find an algebraic expression for the underlined quantity.
The distance, given that the rate is x miles per hour and the time is 8 hours.

Question 10

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.
13y + 4y = 12y

Question 11

Lori built a dog lot for her dog, Chollie, by fencing in a rectangular area of her yard. If Chollie's lot required 60 feet of fence and the length is 10 feet longer than the width, then what are the length and width of Chollie's dog lot?

Question 12

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.
p - 8 = p + 8

Question 13

Solve.
0.2n + 2.4 = 0.6n

Question 14

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.
u + 5u = 6u

Question 15

How many pints of a 9% cleaning solution must be mixed with 2 pints of a 13% cleaning solution to give a 11% solution?

Question 16

Find y given that x = -7 and y = -4x + 5.

Question 17

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity.
80 - 5(t + 4) = 0

Question 18

Ferdinand sold his algebra textbook using an internet auction site that charges a commission of 13% of the selling price. After the commission was paid, Ferdinand received $22.64. If x represents the selling price, then x satisfies x - 0.13x = 22.64. Solve this equation to find the selling price.

Question 19

The law firm of Dewey, Cheetham, and Howe handled 36 personal injury cases this past year. this was of the cases handled by the rival firm of Gypsum-Goode. How many personal injury cases were handled by Gypsum-Goode last year?

Question 20

James paid $234 for a DVD player that was priced originally at $260. What was the discount rate?

Question 21

Graph the inequality:

Question 22

At a 30% discount rate, Jack's discount was more than $12 on the jacket he purchased. Write an inequality to describe this situation using p for the original price of the jacket.

Question 23

The length of a rectangle must be 8 centimeters more than the width, and the perimeter must be at least 36 centimeters. What is the range of values for the width?

Question 24

Graph the inequality: -2 < x < 3

Question 25

Solve and write your solution in interval notation.
-17 < 28 - 9n $\le$ 1

Question 26

Write the appropriate inequality symbol in the blank so that the two inequalities are equivalent.
-55 $\ge$ 5y
-11 _____ y