Name: __________________________ Date: ______________
1. If a television costs $311 after a 35% discount, what was the original cost?
a. $276.00
b. $419.85
c. $888.57
d. $478.46
2. Two cars start from the same point and travel in opposite directions. The rate of the slower car is 15 miles per hour less than the rate of the faster car. After 8 hours they are 840 miles apart. Find the speed of the cars.
a. 90 mph and 75 mph
b. 105 mph and 90 mph
c. 60 mph and 45 mph
d. 100 mph and 85
3. If the smaller of two consecutive odd integers is doubled, the result is 7 more than the larger of the two integers. Find the two integers.
a. 3 and 5
b. 5 and 7
c. 9 and 11
d. 13 and 15
4. The length of a rectangular garden is 8 more meters than its width. Its perimeter is 76 meters. Find the length of the garden.
a. 23 meters
b. 76 meters
c. 345 meters
d. 15 meters
5. If a DVD player costs $306 after a 30% increase in price, what was the original cost?
a. $91.80
b. $214.20
c. $437.14
d. $235.39
6. If 8 times a number is increased by 20, the result is 26 less than the square of the number. Choose the equation that could be used to find this number, x.
a.
b.
c.
d.
7. Identify the proportion listed below that solves the problem: A car can travel 603 miles on 11 gallons of gasoline. How far can the car travel on 36 gallons?
a. c.
b. d.
8. The perimeter of a triangle is 30 inches. The length of the middle side is 2 inches more than the length of the smaller side and the largest side is 4 inches more than twice the length of the smallest side. Find the length of the smallest side.
a. 6 inches
b. 8 inches
c. 4 inches
d. 2 inches
9. Two tuna boats start from the same port at the same time, but they head in opposite directions. The faster boat travels 10 knots per hour faster than the slower boat. At the end of 8 hours, they were 272 nautical miles apart. How many nautical miles had each boat traveled by the end of the 8-hour period?
a. 12 and 22 nautical miles
b. 96 and 176 nautical miles
c. 131 and 141 nautical miles
d. 17 and 27 nautical miles
10. If a student completed this worksheet that covers word problems that are on the state competency exam to pass this class and had some difficulty. Should the student make sure that they ask questions, always go to class, take good notes, complete their homework, and seek extra help when needed?
a. Yes
b. Yes
c. Yes
d. Yes
1. D Check
Original Cost – Discount = Sale Price 478.46 - .35(478.46) = 311
X - .35X = 311 478.46 – 167.46 = 311
1X - .35X = 311 311 = 311
.65X = 311
.65 .65
X = 478.46
________________________________________________________________________
2. C
Type |
D |
R |
T |
Fast Car |
8X |
X |
8 |
Slow Car |
8(X – 15) |
X – 15 |
8 |
Total |
840 |
|
|
Fill in the 4 x 4 chart with the given information.
To fill in the distance column use the formula Distance = Rate x Time
You now have the formula:
8X + 8(X – 15) = 840
Distributive Property: 8X + 8X – 120 = 840
Combine Like Terms: 16X -120 = 840
+ 120 +120
Solve for X: 16X = 960
16 16
X = 60
Substitute X into the chart and answer the question:
Type |
D |
R |
T |
Fast Car |
8(60) = 480 miles |
60 mph |
8 |
Slow Car |
8(60– 15) = 360 miles |
60 – 15 = 45 mph |
8 |
Total |
840 miles |
|
|
3. C
Consecutive Odd Integers Smaller doubled is 7 more than larger number
Small Number: X 2X = 7 + X + 2
Large Number: X + 2 Solve for X: 2X = X + 9
- X - X
Small Number: 9 X = 9
Large Number: 9 + 2 = 11
________________________________________________________________________
4. A
Width: W
W + 8 Length: W + 8
Perimeter: 76
W W
W + 8
Equation: W + W + 8 + W + W + 8 = 76 Width: W = 15
Combine Like Terms: 4W + 16 = 76 Length: 15 + 8 = 23
- 16 - 16
4W = 60 Check: 15 + 23 + 15 + 23 = 76
4 4 76 = 76
Solve: W = 15
________________________________________________________________________
5. D
Original Cost + Increase = New Price Check: 235.39 + .30(235.39) = 306
X + .30X = 306 235.39 + 70.61 = 306
1X + .30X = 306
306 = 306
1.30X = 306
1.30 1.30
X = $235.39
6. B
Translate the problem to:
________________________________________________________________________
7. A
Note: If your proportion does not match the
proportion on the test, multiply the
diagonals to see which matches.
Matches:
________________________________________________________________________
8. A
Small: X
Middle: X + 2
Large: 2X + 4 X X + 2
Perimeter: 30
2X + 4
The equation will be: X + X + 2 + 2X + 4 = 30
Combine like terms: 4X + 6 = 30
Solve: - 6 - 6
4X = 24 Check: 6 + 6 + 2 + 2(6) + 4 = 30
4 4 6 + 8 + 16 = 30
14 + 16 = 30
X = 6 30 = 30
Small: X = 6
Middle: 6 + 2 = 8
Large: 2(6) + 4 = 16
9. B
Type |
D |
R |
T |
Fast Boat |
8(X+10) |
X+10 |
8 |
Slow Boat |
8X |
X |
8 |
Total |
272 |
|
|
Fill in the 4 x 4 chart with the given information.
To fill in the distance column use the formula Distance = Rate x Time
You now have the formula:
8X + 8(X + 10) = 272
Distributive Property: 8X + 8X + 80 = 272
Combine Like Terms: 16X + 80 = 272
-80 - 80
Solve for X: 16X = 192
16 16
X = 12
Substitute X into the chart and answer the question:
Type |
D |
R |
T |
Fast Boat |
8(12 + 10)=176 miles |
12 + 10 = 22 knots |
8 |
Slow Boat |
8(12) = 96 miles |
12 knots |
8 |
Total |
272 miles |
|
|
The answer from the chart is the fast boat traveled 176 miles and the slow boat traveled 96 miles.
________________________________________________________________________
10. UMMMMMMMMMMMMMMMMM!!!!!!! The answer is YES!!!
The competency exam is very important.
To pass MAT0024C Elementary Algebra you need an 80% or better on the competency exam.
Note: Use test taking strategies like eliminating the incorrect answers first, then look at the possible choices.