# systems of linear equations

**Question description**

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

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