systems of linear equations

Sep 2nd, 2015
RockCafe
Category:
Mathematics
Price: $10 USD

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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