**Name:__________________________ Algebra 1: Chapter 3 Test - Study Guide**
**Equations, Proportions, Formulas**
1. Alisha's brother is 6 years younger than Alisha. Alisha is 5 years younger than her sister. Alisha's brother is 10 years old. Write an equation to find how old Alisha and her sister are.
2. The Chin family is having new carpet installed in the dining room. The carpet costs $249 for installation and $9 for each square yard. Find the number of square yards of carpet installed if the total cost is $465. If the Chin family has $500 to spend, can they afford to have 30 square yards of carpet installed?
3. Jorge has 5 more than twice the number of DVDs as Ahmed. Kaitlin has the same number of DVDs as Jorge, which is equal to 3 less than three times as many as Ahmed. How many DVDs does each person have?
4. The formula for the area of a trapezoid is *A* = *h*(), where *h* is the height of the trapezoid and *b*_{1} and *b*_{2} are the lengths of the bases.
Solve the formula for *h*.
Solve the formula for .
5. Solve for .
6.
7.
8.
9.
10. =
11.
12. Will and Jim shared the driving on a trip to a business convention. Will’s average driving speed was 52 miles per hour. Jim averaged 44 miles per hour and drove 2 hours longer than Will. If *x* is the time Will drove, the situation can be modeled by the equation where *d* is the length of the trip in miles. If the trip was 352 miles long, how far did Jim drive?
13. Rachel wants to earn $700 selling 27 knit scarves. She wants to sell each scarf for $3 less than her competitor. If *x* is the price charged by her competitor, write an equation that models the situation?
14. = 38
15.
16. Write as a function of *x*.
17.
18. If the sum of the two angles is 90 degrees, write an equation to find the value of .
19. Gary's cellular phone bill averages $56.35 per month, based on a fixed fee of $29.95 and $0.22 per minute of usage. The phone company has decided to reduce the per-minute charge to $0.18. How much does this change save Gary in an average month?
20. A rental car agency charges $12 per day plus $.10 per mile to rent a certain car. Another agency charges $15 per day plus $.08 per mile to rent the same type of car. How many miles per day will have to be driven for the cost of a car from the first agency to equal the cost of a car from the second agency?
21. A boxing club charges nonmembers $4 per day to workout and $10 per day for equipment rental. Members pay a yearly fee of $400 and a daily fee of $5 for equipment rental. Write and solve an equation to determine how many times you should use the gym to justify membership.
22. –1.1*x* – 4 = 0.8
23. The simple interest *I* on an investment of *P* dollars at an interest rate *r* for *t* years is given by *I* = *Prt*. Find the time it would take to earn $1300 in interest on an investment of $18,000 at a rate of 6.6%.
24.
25.
26. The figure below represents a building in the shape of a hexagon. Using the scale 1 inch = 59 feet, what is the perimeter of the building?
27. A factory that makes remote-control airplanes can paint 14 models with 11.2 ounces of paint. How many models can be painted with 5 pints of paint?
28. The triangle below has a perimeter of 20. Solve for* x. *
29. Solve for .
30. 4.1*x* = 0.7*x* + 25.9
**Algebra 1: Chapter 3 Test - Study Guide**
**Answer Section**
**ESSAY**
1. a. Sample equation: *a* – 6 = 10; 16 years old
b. Sample equation: *s* – 16 = 5
Alisha is the middle child, and she is 16 years old. Her sister is 5 years older than Alisha is so her sister is 21 years old.
2. a.
b. You subtract 249 from both sides. When solving a two-step equation, you perform addition or subtraction operations first; 24 yd^{2}.
c. No. Evaluate the expression for *x* = 30: = 270 + 249 = 519. Since the Chins only have $500 to spend, they cannot afford to have 30 square yards installed.
3. a. Sample answer: Let *x* be the number of DVDs that Ahmed has. Then write expressions for the number of DVDs that Jorge has and that Kaitlin has in terms of *x*. So, Jorge has DVDs, and Kaitlin has DVDs. Then write an equation to show that the two expressions are equal:
b. Ahmed has 8 DVDs, Jorge and Kaitlin each have 21 DVDs;
Sample answer: First solve the equation in part (a) for *x* to find the number of DVDs that Ahmed has.
Use this number to find the number of DVDs Jorge and Kaitlin have:
or
4. a. = *h; *6.5 cm
b. Multiply both sides of the formula by 2, divide both sides by *h*, then subtract *b*_{2} from both sides, resulting in – *b*_{2} = *b*_{1}.
c. 20 cm
d. Yes. Because *b*_{2} = *b*_{1}, use one variable *b* to represent both bases:
*A* = *h*(*b* + *b*) = *h*(2*b*) = *hb*.
**SHORT ANSWER**
5.
6.
7.
8. –5
9.
10.
11.
12.
13.
14. *n* = 10
15. –66
16.
17. 64
18. 62 degrees
19. $4.80
20. 150 miles per day
21. 14*x* + 400 + 5*x*; 45 times
22. –4.36
23. 1.09 years
24. 18
25. -49
26. 1416 feet
27. 100
28. 5
29.
30. *x* = 8 |