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Miscellaneous
Multi-step Equations
Variables on Both Sides
Problem Solving
Solving Inqualities
100
What is the discounted price if an item has an original price of $100 and a discount of 30%?
The discounted price is $70.
100
2p + 1 = 21
p = 10
100
2x = x + 5
x = 5
100
Sara wanted to buy a pair of jeans. She looked online and found a 20% internet only discount. They charged $5 shipping. She paid $37 for the discounted jeans and shipping. If she hadn't had the discount, how much would she have to have had to pay for the jeans including shipping? Show the equation and solve it.
37 = .8 * P + 5 P is the retail price of the jeans only 32 = .8 * p 32/.8 = p $40 = p Full Price = 40 + 5 = $45
100
3x > 9
x > 3
200
Calculate using order of operations 20 + 3(55 - 10) / 3
65
200
7p - 9 = -30
p = -3
200
x + 1 = 3x - 5
x = 3
200
The school hosted a donut eating contest. Jerry holds the record. Let D be the number of donuts he ate for the school record. In the new competition, let's say Mary eats 10 donuts in the first 2 minutes as she tries to tie Jerry's record. Let r be the average number of donuts Mary needs to eat in the remaining time in order to tie or beat Jerry. Write an inequality to represent the situation. Don't solve yet.
D <= 10 + 2r
200
6y - (2y - 5) < 29
y < 6
300
Solve the equation 3x -32 = 25
x = 19
300
2(x + 1) = 18
x = 8
300
2(3c - 8) = -8c - 2
c = 1
300
The school hosted a donut eating contest. Jerry holds the record. Let D be the number of donuts he ate for the school record. In the new competition, let's say Mary eats 10 donuts in the first 2 minutes as she tries to tie Jerry's record. Let r be the average number of donuts Mary needs to eat in the remaining time in order to tie or beat Jerry. Write an inequality to represent the situation. The first record set in 2009 was 58 donuts. How many donuts would Mary have to eat per minute in her remaining time to at least tie the record? Show your work.
58 < = 10 + 2r 58-10 <= 2r 48/2 <= r 24 <= r
300
2 (x + 4) < 6x - 2 - 4x
2x + 8 < 2x - 2 8 < -2 No Solutions
400
Solve the inequality 3x + 5 > 2x ------ 4
x < 1 3x + 5 > 8x -5x + 5 > 0 -5x > -5 (multiply both sides by -1/5 so flip the symbol) x < 1
400
6(t - 3) = -60
t = -7
400
-2(-7a + 4) = 5(a - 16)
a = -8
400
Mary eats 10 donuts in the first 2 minutes as she tries to tie Jerry's record. Let r be the average number of donuts Mary needs to eat in the remaining time in order to tie or beat Jerry. The first record set in 2009 was 58 donuts. If Mary maintains the beginning pace for the entire 10 minutes would she tie, break or fall short of the record? Explain and show your work.
10 donuts/2 minutes = 5 donuts/1 minute 10 minutes * 5 donuts/1 minute = 50 donuts She would fall short of the record
400
2x + 4 > 4x - 7 - 2x
All Real numbers (Infinite number of solutions)
500
Solve the inequality 9x + 15 < 24 + 10x
x > -9
500
5y + 5(y - 3) = -63
y = -24/5 or -4.8
500
A = ((L+w)/2) * h Rearrange to solve for l
l = 2A/h - w A/h = (l + w)/2 2A/h = l + w l = 2A/h - w
500
You are building a square pen for some pigs. The pen is 576 square yards. You have 325 feet of fencing to build it with. Do you have enough fencing? Why? How much do you need? Show your work.
Yes. If you have 576 square yards then each side of the square pen should be 24 yards because 24 times 24 is 576 square yards. That means each side is 81 feet (3 times 24 yards is 81 feet). Perimeter of a square is 4 times one side. 4 times 81 is 324 feet. We would need 324 feet and we have 325 feet so we would have enough fencing.
500
a (x + b) > c where a doesn't equal 0 Solve for x
x > (c/a) - b