Solving Equations
6.25x + 11 = 23.5
x = 2
12 < 3x + 6
2 < x
solve for b
a + b = c
b = c - a
Andrew makes $9.00 per hour at his job. Write an equation that can be used to find out how many hours, h, he have to work in order to earn $58.50?
9h = 58.5
Sue and James have $20 left for a cab fare home. The cab fare is $3 per mile plus a $2 fixed charge. Write an inequality that could be used to find the maximum number of miles they will be able to travel in the cab?
2 + 3m ≤ 20
-2x + 7 = -x - 5
x = 12
2.85 + 5x < 15x - 4.17
0.702 < x
solve for a:
ra + d = z
a = z/r - d/r
Samantha takes an uber to the airport. The uber charges $5 for the first mile and the $0.75 for each additional mile. Write an equation, where m represents the number of additional miles, that will determine how far Samantha can travel with $25.
5 + 0.75m = 25
Brett has a $30 online gift voucher. He plans to buy as many books as he can. The cost of each book is $4. There is also a single shipping charge of $2. Write an inequality that can be used to find out how many books can he afford without spending more than his gift voucher amount.
4b + 2 ≤ 30
5x + 12 = 3x - 6
x = -9
3x + 5 ≤ 5x - 13
x ≥ 9
solve for b:
db - gb = t
b = t/(d-g)
Mary is baking a cake for a wedding. She is charging the bride and groom an upfront fee of $55 and then $2.50 for each slice of cake needed. Write an equation to determine how many slices of cake the couple can ask for with a budget of $250.
55 + 2.5x = 250
Bert already has $50 but needs a total of at least $250 for his holiday. He gets paid $20 per day for delivering papers. Write an inequality that could be used to find the least number of days he must work to get enough money for his holiday?
50 + 20d ≥ 250
-3(4x - 2) = (1/2)(5 + 4x)
x = 1/4
-2x + 11 < -5(-x + 2)
x > 3
solve for y:
(y + x)/z = f
y = fz - x
The temperature in Moscow was 7 degrees celsius and then started dropping at a steady rate of 1.5 degrees per hour. Write an equation in terms of h (hours) that can be used to determine how many hours would have to pass for the temperature to reach -2 degrees celsius.
7 - 1.5h = -2
Jennifer is planning a holiday. The hotel costs $60 per night and her flights cost $150. She has a budget of $500 for hotel and flights. Write an inequality that can be used to find out up to how many nights she can afford in the hotel.
60n + 150 ≤ 500
(1/4)(x - 5) = (1/3)(2x + 5)
x = -7
(-1/4)(x + 7) ≥ 2 - x
5 ≤ x
solve for x:
(f - t)/x = y
x = f/y - t/y
Joe was deep sea scuba diving in Australia. At 3pm he was scuba diving 40 feet below sea level. He then started to descend at a steady rate of 12 feet per minute. Write an equation in terms of x that can determine how many minutes it will take Joe to reach a depth of 100 feet below sea level.
-40 - 12m = -100
Commission or salary: Jill has a job offer. She is offered either $50 per day or $30 per day plus a commission of $3 for every plant she sells. Write an inequality to find out how many plants she needs to sell to make the commission offer the better option.
30 + 3p > 50