# MTH208 Week 4 Homework Assignment Quiz Solution Key

**MTH208 R4 Week 4 Problem Set V41**

You can use your books, notes, ALEKS, the Center for Math Excellence and/or a calculator, but you must work on your own.

Solve each system of equation by graphing.

- y = x – 3 and y = -x + 1

On graph, x = 2 and y = -1

**Solution Set: (2,-1)**

- 3x - 2y = 6 and 3x + 2y = 6

y = -3/2x + 3

On graph, x = 2 and y = 0

**Solution Set: (2,0)**

3. Solve using the substitution method.

y = -4x – 7

y = 3x

3x = -4x – 7

7 = -7x

**x = - 1**

y = 3x

**y = -3**

**Solution Set: (-1,-3)**

4. Solve using the addition method:

x - y = 12

__2x + y = 3__

3x = 15

**x = 5 **

5 – y = 12

**y = -7**

** Solution Set: (5,-7)**

5. If you have 52 coins consisting only of pennies and nickels, and the total value of the coins is $1.20, how many of each type of coin do you have?

**MTH208 R4 Week 4 Team Problem Set V44**

Solve using the substitution method.

1. 2y = x + 6

-3x + 2y = -2

x = 2y – 6

-3(2y – 6) + 2y = -2

-6y +18 + 2y = -2

-4y = -20

**y = 5**

x = 2(5) - 6

**x = 4**

**Solution Set: (4, 5) **

2. x = -3y + 2

7y = 3x

7y = 3(-3y + 2)

7y = -9y + 6

16y = 6

**y = 3/8**

x = -3(3/8) + 2

x = -9/8 + 2

**x = 7/8**

**Solution Set: (7/8, 3/8) **

** **

3. The graph below shows the cost of producing textbooks and the revenue from the sale of those textbooks.

- What is the cost of producing 9 text books?

C = 10(9) + 150

C = 240

**Cost = $240.00**

- What is the revenue when 12 text books are sold?

R = 25(12)

R = 300

**Revenue = $300.00**

- What number of text books must be sold for the cost to be equal to the revenue?

25x = 10x + 150

15x = 150

x = 10

Costs equal revenue after **10 books** are sold.

- What is the fixed cost, the cost of producing no text books?

**Fixed Cost (b) = $150.00 **

Solve using the addition method:

4. x/3 – y/2 = -5/6

x/5 – y/3 = -3/5

10x – 15y= -25

6x– 10y = -18

6x = 10y – 18

x = 5/3y – 3

???? Not sure on this one????

5. Bernie has 187 cars and motorcycles. When he counted the tires, he found that he has 588 tires on all these vehicles. If each car has 4 tires and each motorcycle has 2 tires, how many cars and how many motorcycles does he have?

x + y = 187

4x + 2y = 588

x = - y + 187

4(-y + 187) +2y = 588

-2y + 748 = 588

-2y = -160

y = 80

x + 80 = 187

x = 107

**Cars (x) = 107**

**Motorcycles (y) = 80**

10. If it takes 500 feet of fencing to enclose a rectangular plot that has a width of 50 feet, then what is the length of the plot?

2(50) + 2x = 500

100 + 2x = 500

2x = 400

x = 200