4.1
4.2
4.3
4.4
4.7
100
Determine whether (-2, -1) is a solution to the system x−y=−12 & x−y=−5
(-2, -1) is not a solution.
100
The sum of two numbers is zero. One number is nine less than the other. Find the numbers.
9/2 and −9/2
100
Justin has a pocketful of nickels and dimes. The total value of the coins is $8.10. The number of dimes is 9 less than twice the number of nickels. How many nickels and how many dimes does Justin have?
Justin has 36 nickels and 63 dimes
100
Determine whether the ordered triple is a solution to the system: x−y+z=2 & 2x−y−z=−6 & 2x+2y+z=−3.
(−2,−1,3)
(−2,−1,3) is a solution
100
Determine whether (−2,4) is a solution to the system x+4y≥10 & 3x−2y<12
(−2,4) is a solution
200
Solve the system by graphing 2x+y=7 & x−2y=6
(4, -1)
200
Jessi has been offered two options for her salary as an acting coach. Option A would pay her $25,000 plus $15 for each client. Option B would pay her $10,000 plus $40 for each client. How many clients would make the salary options equal?
600 clients
200
Carson wants to make 20 pounds of trail mix using nuts and chocolate chips. His budget requires that the trail mix costs him $7.60. per pound. Nuts cost $9.00 per pound and chocolate chips cost $2.00 per pound. How many pounds of nuts and how many pounds of chocolate chips should he use?
Carson should mix 16 pounds of nuts with 4
pounds of chocolate chips to create the trail
mix
200
Solve the system by elimination: x−2y+z=3 & 2x+y+z=4 & 3x+4y+3z=−1
(4, -1, -3)
200
Solve the system by graphing: x−y>3 & y<−1/5x+4
300
Solve the system by substitution: 4x+2y=46 & x−y=8
(5/4, -1/2)
300
When Jamie spent 10 minutes on her math homework and then worked on a science project for 20 minutes, she earned 278 points on her school work tracker. When she spent 20 minutes on math homework and 30 minutes on a science project, she earned 473 points. How many points does she earn for each minute spent on math? How many points for each minute of her science project?
Jamie earns 8.3 points per minute
spent on science, and 11.2 points per
minute spent on math.
300
Sasheena is lab assistant at her community college. She needs to make 200 milliliters of a 40% solution of sulfuric acid for a lab experiment. The lab has only 25% and 50% solutions in the storeroom. How much should she mix of the 25% and the 50% solutions to make the 40% solution?
Sasheena should mix 80 ml of the 25% solution with
120 ml of the 50% solution to get the 200 ml of the
40% solution.
300
Solve: 3x−4z=0 & 3y+2z=−3 & 2x+3y=−5.
(-4, 1, -3)
300
Solve the system by graphing: 4x+3y≥12 y<−4/3x+1
There is no solution
400
Solve using elimination: x+1/2y=6 & 3/2x+2/3y=17/2.
(3, 6)
400
Translate to a system of equations and then solve.
The difference of two complementary angles is 26 degrees. Find the measures of the angles.
(Complementary angles add up to 90 degrees)
The angle measures are 58 and 32 degrees
400
Adnan has $40,000 to invest and hopes to earn 7.1%7.1% interest per year. He will put some of the money into a stock fund that earns 8% per year and the rest into bonds that earns 3% per year. How much money should he put into each fund?
Adnan should invest $32,800 in stock and
$7,200 in bonds
400
Solve the system of equations: x+2y−3z=−1 & x−3y+z=1 & 2x−y−2z=2
We are left with a false statement and this tells us the system is inconsistent and has no solution.
400
Solve the system by graphing: y>12x−4 & x−2y<−4
500
Decide whether substitution or elimination is easier for this equation. 3x+8y=40 & 7x−4y=−32
Since both equations are in standard form, using elimination will be most convenient.
500
A river cruise ship sailed 60 miles downstream for 4 hours and then took 5 hours sailing upstream to return to the dock. Find the speed of the ship in still water and the speed of the river current.
The rate of the ship is 13.5 mph and
the rate of the current is 1.5 mph.
500
The manufacturer of a weight training bench spends $105 to build each bench and sells them for $245. The manufacturer also has fixed costs each month of $7,000
ⓐ Find the cost function C when x benches are manufactured.
ⓑ Find the revenue function R when x benches are sold.
ⓒ Show the break-even point by graphing both the Revenue and Cost functions on the same grid.
ⓓ Find the break-even point. Interpret what the break-even point means.
When 50 benches are sold, the revenue and costs are both $12,250. Notice this corresponds to the ordered pair (50,12,250).
500
The LCA theater department sold three kinds of tickets to its latest play production. The adult tickets sold for $15, the student tickets for $10 and the child tickets for $8. The theater department was thrilled to have sold 250 tickets and brought in $2,825 in one night. The number of student tickets sold is twice the number of adult tickets sold. How many of each type did the department sell?
The theater department sold 75 adult tickets,
150 student tickets, and 25 child tickets.
500
Omar needs to eat at least 800 calories before going to his team practice. All he wants is hamburgers and cookies, and he doesn’t want to spend more than $5. At the hamburger restaurant near his college, each hamburger has 240 calories and costs $1.40. Each cookie has 160 calories and costs $0.50.
ⓐ Write a system of inequalities to model this situation.
ⓑ Graph the system.
ⓒ Could he eat 3 hamburgers and 1 cookie?
ⓓ Could he eat 2 hamburgers and 4 cookies?
ⓐ
240h+160c≥800
1.40h+0.50c≤5
h≥0
c≥0
ⓑ
ⓒ Omar might choose to eat 3 hamburgers and 1 cookie.
ⓓ Omar might choose to eat 2 hamburgers and 4 cookies.