systems of linear equations
Three times one number minus a second is 8, and the sum of the numbers is 12. Which system of equations could be used to find the two numbers?
o 3x – y = 8
xy = 12
o 3x – y = 8
x + y = 12
o y – 3x = 8
xy = 12
o y – 3x = 8
x + y= 12
One number is two more than a second number. Twice the first is 4 less than 3 times the second. Find the two numbers.
o 3 and 4
o 8 and 10
o 0 and 2
o 1.6 and 3.6
Find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 60 quarts of 2% butter fat milk.
o 20 quarts of 4% and 40 quarts of 1%
o 40 quarts of 4% and 20 quarts of 1%
o 60 quarts of 4% and 0 quarts of 1%
o 30 quarts of 4% and 30 quarts of 1%
The Fabulous Footballers scored an incredible 55 points at last night’s game. Interestingly, the number of field goals was 1 more than twice the number of touchdowns. The Fabulous Footballers earned 7 points for each touchdown and 3 points for each field goal.
Which of the following systems of equations models this situation when t represents the number of touchdowns and f represents the number of field goals?
o t = 2f + 1
7t +3f = 55
o f = 2 t + 1
t + 3f = 55
o t = 2f +1
3t + 7f = 55
o f =2t +1
3t + 7f = 55
Taylor and Jeff have been selling frozen pizzas for a class fundraiser. Taylor has sold half as many pizzas as Jeff. Together they have sold a total of 126 pizzas. How many pizzas did Taylor sell?
o 21
o 42
o 63
o 84
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
o $1.50
o $2.00
o $3.00
o $3.50
Find the values of x and y in the following isosceles triangle.
o x = 47.5, y = 66.25
o x = 0, y = 190
o x = 5, y = 175
o x = 40, y = 70
How many units of x must be sold to break even if the cost function is C(x) = 30x + 10,000 and the revenue function is R(x) = 46x? Round to the nearest unit, if necessary.
o 132 units
o 625 units
o 333 units
o 6522 units
How many units of x must be sold to break even if the cost function is C(x) = 0.8x + 900 and the revenue function is R(x) = 2x? Round to the nearest unit, if necessary.
o 432 units
o 321 units
o 750 units
o 450 units
The planning department of Abstract Office Supplies has been asked to determine whether the company should introduce a new computer desk next year. The department estimates that $6000 of new manufacturing equipment will need to be purchased and that the cost of constructing each desk will be $200. The department also estimates that the revenue from each desk will be $450.
Which cost function C(x) and revenue function R(x) can be used to model this scenario?
o C(x) =6000x + 200
R(x) = 450x
o C(x) = 200x + 6000x
R(x) = 450x
o C(x) = 450x + 6000
R(x) = 200x
o C(x) = 200x + 6000
R(x)= 450x
