Linear Equations
Your math teacher tells you next week's test is worth 100 points. Each problem is worth either 5 points or 2 points. There is a total of 26 questions on the test. Write the system of Linear equations to model this situation.
x+y=26
5x+2y=100
You can work a total of no more than 41 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $254 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.
x+y<=41
5x+8y>=254
I bought a car for $25,000, but its value is depreciating at a rate of 10% per year. How much will my car be worth after 8 years?
25,000(0.9)^8 = 10,761.68025
$10,761.68
A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. Find the starting height of the ball. The equation that gives the height (h) of the ball at any time (t) is:
h(t) = -16t^2+40t+2
2 feet
Student tickets to a school play cost $6. Non‑student tickets cost $10. 360 people attended the school play, paying a total of $2,780. How many students attended the play?
205 students attended the play
Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She is only allowed to work 13 hours per week. She wants to make at least $65. Write a system of inequalities to represent this situation.
4x+7y>=65
x+y<=13
You deposit $1500 in an account that pays 5% interest compounded yearly. Find the balance after 6 years.
1500(1.05)^6 = 2,010.143461
$2010.14
A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. Find the maximum height of the ball. The equation that gives the height (h) of the ball at any time (t) is:
h(t) = -16t^2+40t+2
27 feet
Sam has a jar of nickels and dimes. The jar has 20 coins in it and a total value of $1.40. How many nickels and how many dimes are in the jar?
12 nickels and 8 dimes
Sue is buying T-shirts and shorts. T-shirts cost $14 and shorts cost $21. She plans on spending no more than $147 and buy at least 5 items. Show and describe all combinations of the number of T-shirts and shorts she could buy.
14x+21y<=147
x+y>=5
You deposit $1500 in an account that pays 5% interest compounded monthly. Find the balance after 6 years.
1,500(1+.05/12)^(6*12) = 2023.526616
$2023.53
A diver is standing on a platform 24 ft. above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Find the time that the diver reaches their maximum height. The equation that gives the height (h) of the diver at any time (t) is:
h(t) = -16t^2+8t+24
0.25 seconds
A Beach Hotel in Cancun is offering two weekend specials. One includes a 2-night stay with 3 meals and cost $195. The other includes a 3-night stay with 5 meals and cost $300. What is the cost of a single meal?
$15 for one meal
A student has to buy graph paper and printer paper. The printer paper costs $2 a pack, while the graphing paper costs $3 a pack. She wants to buy at least 6 packs of paper but wants to spend at most $27.
2x+3y<=27
x+y>=6
You deposit $98,000 in an account in 2005 that pays 11% interest compounded semiannually. Find the balance in 2021.
98,000(1+.11/2)^(2*16) = 543,631.7135
$543,631.71
A diver is standing on a platform 24 ft. above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Find the time that the diver will be 16ft in the air. The equation that gives the height (h) of the diver at any time (t) is:
h(t) = -16t^2+8t+24
1 second
In an aquarium, there are some lobsters and some fish (and nothing else). Altogether, there are 400 legs and 70 tails. How many lobsters and how many fish are in the aquarium? (Lobsters have ten legs and a tail. Fish have zero legs and a tail.)
A food truck sells Tacos for $4 and burritos for $5 each. The food truck needs to make at least $400 today. The food truck is running low on burrito wraps so it can't sell more that 10 burritos. Write a system of linear inequalities that describes the situation and solve for the minimum number of tacos the food truck must sell to reach its goal if it sells out of burritos.
4x+5y>=400
y<=10
88 Tacos
The number of mosquitoes at the beach has tripled every year since 1999. In 1999, there were 2,500 mosquitoes. Write a model for this situation. How many mosquitoes would you predict were at the beach in 2005?
y=2500(3)^x
2500(3)^6=1,822,500
A diver is standing on a platform 24 ft. above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Find the time that the diver will hit the water. The equation that gives the height (h) of the diver at any time (t) is:
h(t) = -16t^2+8t+24
1.5 seconds