Solving Equations
9x + 1 = 10
x = 1
Margo can purchase tile at a store for $0.79 per tile and rent a tile saw for $24. At another store, she can borrow the tile saw for free if she buys tiles there for $1.19 per tile. Write an equation to find the number of tiles she must buy for the cost to be the same at both stores.
0.79x + 24 = 1.19x
A yellow hot-air balloon is 100 feet off the ground and rising at a rate of 8 feet per second. An orange hot-air balloon is 160 feet off the ground and rising at a rate of 5 feet per second. Write an inequality to find out how long will the yellow balloon be higher than the orange balloon after x, seconds?
8x + 100 > 5x + 160
Sandy is upgrading her internet service. Fast Internet charges $60 for installation and $50.45 per month. Quick Internet has free installation but charges $57.95 per month. After how many months, x, will both internet services cost the same.
x = 8
12x + 12 = 3x + 84
x = 8
A water tank holds 256 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 384 gallons but is leaking at a rate of 5 gallons per week. Write an equation to find the number of weeks needed for the amount of water in the two tanks to be the same.
256 - 3x = 384 - 5x
A rose bush is 4.5 inches tall and grows 0.75 inches per week. A sunflower is 3 inches tall and grows 1 inch per week. Write an inequality to represent the weeks it will take for the rose bush to be less than the sunflower.
0.75x + 4.5 < x + 3
A 12 inch candle and an 18 inch candle are lit at 6pm. The 12 in candle burns 0.5 in every hour. The 18 in candle burns 2 in every hour. After how many hours, h, will the candles be the same height?
h = 4
6x + 7 = 13 + 7x
x = -6
Country Carpets charges $22 per square yard for carpeting, and an additional installation fee of $100. City Carpets charges $25 per square yard for the same carpeting, and an additional installation fee of $70. Write an equation to find the number of square yards of carpeting for which the total cost charged by the two companies will be the same.
22x + 100 = 25x + 70
The Daily Record charges a fee of $525 plus $75 per week to run an ad. The Chronicle charges $150 per week. Write an inequality that can be solved to find the number of weeks an ad must run to make the total cost of running an ad in The Daily Record less than the cost in The Chronicle.
75x + 525 < 150x
Andy’s Rental Car charges an initial fee of $20 plus an additional $30 per day to rent a car. Buddy’s Rental Car charges an initial fee of $36 plus an additional $28 per day. After how many number of days, x, would the total cost charged by the companies be the same?
x = 8
0.4x + 7 = 0.5x - 6
x = 130
Jerry has a new job and earns a salary of $45,000. Victoria has a new job and earns a salary of $54,000. Jerry will receive a salary increase of $2,500 per year, and Victoria will receive a salary increase of $1,500 per year. Write an equation that can be used to find x, the number of years it will take Jerry to earn the same salary as Victoria.
2,500x + 45,000 = 1,500x + 54,000
The temperature in Amarillo is 74 °F and is increasing at a rate of 2 °F per hour. In Houston, it is 68 °F and increasing 4 °F per hour. Write an inequality to find how long it will take for the temperature in Houston to exceed the temperature in Amarillo.
4x + 68 > 2x + 74
Container A and container B have leaks. Container A has 800 ml of water, and is leaking 6 ml per minute. Container B has 1000 ml, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
x/4 + 5 = 6 - x/8
x = 8/3
Members of the Wide Waters Club pay $105 per summer season, plus $9.50 each time they rent a boat. Non-members must pay $14.75 each time they rent a boat. Write an equation to find the number of times a member and a non-member have to rent a boat in order to pay the same amount.
9.50x + 105 = 14.75x
Two water tanks hold 28.62 gallons and 31.2 gallons of water. The larger tank is leaking at a rate of 0.12 gallon per hour. The smaller tank is leaking at a rate of 0.08 gallon per hour. Write an inequality that represents how many hours there will be less water in the larger tank than in the smaller tank after x, hours.
31.2 - 0.12x < 28.62 - 0.08x
UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many pounds, p, will it take for UPS and FedEx to cost the same?
p = 20