Algebra Expect For Homework

My Homework Assignment For Module Seven

Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

1. Solve the system by addition.

x + 4y = 2

3x – 2y = –22

X=-6, y=2

2. Solve the system by addition.

x + y = 8

x – y = 8

2x=16

X=8

Y=0

3. Solve the system by addition.

5x – 3y = 13

4x – 3y = 11

5x-4x=2

X=2

Y=-1

4. The sum of two numbers is 33. Their difference is 7. What are the two numbers?

x+y=33

x-y=7

Add

2x=40

X=20

Y=13

5. Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum and paid $2.00. Find the cost of a chocolate bar and the cost of a pack of gum.

3x+y=1.75

2x+4y=2

X=.5

Y=.25

6. Adult tickets for a play cost $16 and child tickets cost $6. If there were 25 people at a performance and the theater collected $260 from ticket sales, how many adults and how many children attended the play?

x+y=25

16x+6y=260

X=11, y=14

7. Solve the system by substitution.

x + 3y = –4

2x + 2y = –8

2(-4-3y) + 2y = -8

Y=0

X=-4

8. The difference of two numbers is 36. The larger is 6 less than 4 times the smaller. What are the two numbers?

x-y=36

x = 4y-6

x=50

y=14

9. The base of a ladder is 6 feet away from the wall. The top of the ladder is 7 feet from the floor. Find the length of the ladder to the nearest thousandth.

Sqrt(49+36) = 9.22 ft

10. A company produces doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets.

x >= 20 y >= 10 3x + 8y <= 400 x + y <= 100