Solving Equations
Literal Equations and Formulas
Solving Linear Inequalities
Word Problems of Linear Equations
Word Problems of Linear Inequalities
100
-2.5 = x - 7.1
What is 4.6
100
The formula for the area of a triangle
What is bh/2
100
3/5 + x < 13/5
What is x < 2
100
Costumes for a play at a community theater cost $1500, which is one third of the total budget. What is the total budget for the play?
What is $4500.
100
The hard drive on your computer has a capacity of 120GB. You have used 85GB. You want to save some home videos to your hard drive. What are the possible sizes of the home video collection you can save?
What is Any size less than or equal to 35GB.
200
(x + 17)/2 = 16/3 in improper fraction. ( / means a fraction bar.)
What is -19/3
200
x/a = y/b (solve for x)
What is x = ay/b
200
-5x < 65
What is x > -13
200
Two college friends rent an apartment. They have to pay the landlord two months' rent and a $500 security deposit when they sign the lease. The total amount they pay the landlord is $2800. What is the rent for one month?
What is $1150.
200
The student council wants to rent a ballroom for the junior prom. The ballroom's rental rate is $1500 for 3 hours and $125 for each additional half hour. Suppose the student council raises $2125. What is the maximum number of hours for which they can rent the ballroom?
What is 5.5 hours
300
0.25 (x - 12) = 4
What is 28
300
4 (x - b) = x (Solve for x)
What is x = 4b/3
300
17 - (4k - 2) > 2(k + 3)
What is k < 13/6
300
Martha takes her niece and nephew to a concert. She buys T-shirts and bumper stickers for them. The bumper stickers cost $1 each. Martha's niece wants 1 shirt and 4 bumper stickers, and her nephew wants 2 shirts but no bumper stickers. If Martha's total is $67 what is the cost of one shirt?
What is $21.
300
The acidity of the water in a swimming pool is considered normal if the average of three pH readings is between 7.2 and 7.8 inclusive. The first two readings for a swimming pool are 7.4 and 7.9. What possible values for the third reading p will make the average pH normal?
What is Between 6.3 and 8.1, inclusive.
400
h/2 + (h-6)/3 = 5h/6 + 2
What is no solution
400
A vehicle travels on a highway at a rate of 65mi/h. How long does it take the vehicle to travel 25 mi?
What is 0.4h
400
-4/3 < w/7 - 3/4 < 1
What is -49/12 < w < 49/7
400
Write and solve an equation to find three consecutive even numbers which add up to 1524.
What is x + (x+2) + (x+4) = 1524; 506, 508, 510.
400
Recommended heart rates during exercise vary with age and physical condition. For healthy person doing moderate to intense exercise such as hiking, the inequality 0.5 (220 - a) <= R <= 0.9 (220 - a) gives a target range for the heart rate R (in beats per minutes) based on age a (in years). What is the target range for heart rates for a person 15 years old?
What is 102.5 <= R <= 184.5
500
2.25 (4x - 4) = -2 + 10x + 12
What is -19
500
Bricklayers use the formula n = 7lh to estimate the number n of bricks needed to build a wall of length l and height h, where l and h are in feet. Solve the formula for h and estimate the height of a wall 28 ft long that requires 1568 bricks. (Points are given when both answers are correct.)
What is h= n/7l; 8 ft
500
12h - 3 > 15h OR 5 > -0.2h + 10
What is h < -1 OR h> 25
500
Suppose a family drives at an average rate of 60mi/h on the way to visit relatives and then at an average rate of 40 mi/h on the way back. The return trip takes 1 hour longer than the trip there. Write and solve an equation to determine the distance the family drove to see their relatives. (Points are given when you write correct equation and answer!)
What is d/60 + 1 = d/40; 120 mi
500
Bonus Question: Text messages cost $0.15 each. You can spend no more than $10. How many text messages can you spend?
What is no more than 66 text messages.
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