Solving Equations
Solve for x.
x - 3 = 90
x = 93
Solve for x.
2x - 3 = x + 7
x = 10
A movie theater sells chocolate bars for $4.00 each. If the theater made $200.00 in one day just from selling chocolate bars, how many bars, x, did the theater sell?
Write an equation to represent this situation.
4x = 200
Gym A charges $40 a month plus $75 at the start of each year. Gym B charges $30 a month plus $90 at the start of each year. Write an equation to compare the costs of both gyms after x months.
40x + 75 = 30x + 90
Solve the following equation for y.
ax + y = b
y = b - ax
Solve for x.
9x + 11 = 110
x = 11
Solve for x.
(1/2)x + 19 = (1/4)x + 45
x = 104
Write an equation to represent this situation.
4.50x + 6.50 = 29.00
Jerry's lemonade stand sells lemonade for $1.50 a glass and charges a one-time fee of $3.00. Kelly's lemonade stand sells lemonade for $2.50 a glass and charges a one-time fee of $2.00. Kelly's lemonade stand is running a deal today for 25% off of your total. How many glasses of lemonade, x, you need to buy to spend the same amount at both stands?
Write and solve an equation to represent this.
1.5x + 3 = (0.75)(2.5x + 2)
Solve the following literal equation for w.
P = 2L + 2w
w = (1/2)(P - 2L)
or w = (P/2) - L
Solve for x.
(2/5)x + 3.5 = 14.6
x = 27.75 or 27 3/4 or 111/4
Solve for x.
3x - 14 = 2(1.5x - 7)
Infinitely many solutions.
Edgar sells a dozen homemade cookies for $6.00 a box. He also charges $1.50 as tax at the end of the order. His close friend Jenna buys some boxes of cookies and spends $9.75 after Edgar gives her a 50% discount. How many boxes of cookies, x, did she buy?
Write an equation to represent this situation.
(0.5)(6x + 1.5) = 9.75
OR
3x + 0.75 = 9.75
Jeffery sells x mini wood figures at $5.00 each and 6 glass figures at $7.00 each. The average cost of one figure is $6.00. How many figures did Jeffery sell?
Write an equation to represent this situation.
5x + 42 = 6(x + 6)
Solve the following literal equation for r.
F = (G(m1m2))/r2
r = √ ((Gm1m2)/F)
Solve for x.
3(x - 9) = 27
x = 18
Solve for x.
13x + 90 = 4(3.25x - 22.5)
No solution.
Marie has 9 full cases of water bottles and 13 loose water bottles. If she has a total of 94 bottles, which equation can be used to find the number of bottles, x in each case?
9x + 13 = 94
Mariah has 6 cups of chocolate ice cream that she sells at $6.50 a cup and x cups of vanilla ice cream that she sells at $5.00 a cup. She wants to sell a chocolate-vanilla swirl ice cream at $6.00 a cup. How many cups of vanilla ice cream does she need to do this?
Write an equation to represent this situation.
39 + 5x = 6(x + 6)
Solve the following literal equation for b.
a2 + b2= c2
If a = 4 and c = 5, solve for b.
b = √(c2 - a2)
b = 3
Solve for x.
(4/9)(x + 4.5) = 9.7
x = 17.325
Solve for x.
0.5(2x - 19) = 0.25(6x - 38)
x = 0
The sum of three consecutive odd integers is 99. What are the three integers?
Write an equation that would help you figure out the values of the three integers.
x + (x + 2) + (x + 4) = 99
Steve and Alice are doing yard work for a landscaping company. Steve digs up 3 patches of dirt a minute, while Alex digs up 6 patches of dirt a minute. If Steve has already dug up 42 patches of dirt and Alex has already dug up 27, how many minutes, x, will it take for them to dig up the same total number of dirt patches?
Write an equation to represent this situation.
3x+ 42 = 6x + 27
Solve the following literal equation for h.
V = (1/3)πr2h
If r = 5 and V = 50π, solve for h.
(3V)/(πr2) = h
h = 6