Name: __________________________ Date: ______________
1. If a sony play station costs $250 after a 15% discount, what was the original cost?
a. $294.12
b. $212.50
c. $287.50
d. $399.46
2. Two formula one racecars start from the same point and travel in opposite directions. The rate of the slower car is 25 miles per hour less than the rate of the faster car. After 10 hours they are 2250 miles apart. Find the speed of the slow car.
a. 125 mph
b. 100 miles
c. 1000 mph
d. 100 mph
3. If the smaller of two consecutive even integers is doubled, the result is 10 more than the larger of the two integers. Find the larger integer.
a. 4
b. 8
c. 14
d. 15
4. The width of a rectangular garden is 8 meters less than its length. 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 palm pilot costs $1300 after a 20% increase in price, what was the original cost?
a. $1625.00
b. $1083.33
c. $1560.00
d. $1040.00
6. If 10 times a number is decreased by 29, the result is the product of 42 and 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 1200 miles on 60 gallons of gasoline. How many gallons do you need to travel 100 miles?
a.
c.
b.
d.
8. The perimeter of a triangle is 51 inches. The length of the middle side is 5 inches more than the length of the smaller side and the largest side is 4 inches less than three times the length of the smallest side. Find the length of the middle side.
a. 10 inches
b. 15 inches
c. 26 inches
d. 5 inches
9. Two shrimp boats start from the same port at the same time, but they head in opposite directions. The slower boat travels 15 knots per hour slower than the fast boat. At the end of 12 hours, they were 600 nautical miles apart. How many nautical miles had the slow boat traveled by the end of the 12-hour period?
a. 210 nautical miles
b. 17.5 nautical miles
c. 2.5 nautical miles
d. 390 nautical miles
10. If a student had some difficulty completing this worksheet that covers word problems that are on the state competency exam, that is REQUIRED to pass this class and the student wanted to do well on the competency exam, what should the student do?
a. Ask questions
b. Always go to class and take good notes
c. Complete their homework
d. Seek extra help when needed like the instructor and the tutoring center (1-131)
e. ALL THE ABOVE!!!!
1. A Check
Original Cost – Discount = Sale Price 294.12 - .15(294.12) = 250
X - .15X = 250 294.12 – 44.12 = 250
1X - .15X = 250 250 = 250
.85X = 250
.85 .85
X = 294.12
________________________________________________________________________
2. D
|
Type |
D |
R |
T |
|
Fast Car |
10X |
X |
10 |
|
Slow Car |
10(X – 25) |
X – 25 |
10 |
|
Total |
2250 |
|
|
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:
10X + 10(X – 25) = 2250
Distributive Property: 10X + 10X – 250 = 2250
Combine Like Terms: 20X -250 = 2250
+ 250 +250
Solve for X: 20X = 2500
20 20
X = 125
Substitute X into the chart and answer the question:
|
Type |
D |
R |
T |
|
Fast Car |
10(125) = 1250 miles |
125 mph |
10 |
|
Slow Car |
10(125– 25) = 1000 miles |
125 – 25 = 100 mph |
10 |
|
Total |
2250 miles |
|
|
3. C
Consecutive Even Integers Smaller doubled is 10 more than larger number
Small Number: X 2X = 10 + X + 2
Large Number: X + 2 Solve for X: 2X = X + 12
- X - X
Small Number: 12 X = 12
Large Number: 12 + 2 = 14
________________________________________________________________________
4. A
W - 8 Width: W -8
Length: W
W W
Perimeter: 76
W - 8
Equation: W + W - 8 + W + W - 8 = 76 Width: 23 – 8 = 15
Combine Like Terms: 4W - 16 = 76 Length: 23
+ 16 +16
4W = 92 Check: 15 + 23 + 15 + 23 = 76
4 4 76 = 76
Solve: W = 23
________________________________________________________________________
5. B
Original Cost + Increase = New Price Check: 1083.33 + .20(1083.33) = 1300
X + .20X = 1300
1X + .20X = 1300 1083.33 + 216.67 = 1300
1300 = 1300
1.20X = 1300
1.20 1.20
X = $1083.33
6. B
Translate the problem to:
________________________________________________________________________
7. B
Note: If your proportion does not match the
proportion
on the test, multiply the
diagonals to see which matches.
________________________________________________________________________
8. B
Small:
X
Middle: X + 5
Large: 3X - 4 X X + 5
Perimeter: 51
3X - 4
The equation will be: X + X + 5 + 3X - 4 = 51
Combine like terms: 5X + 1 = 51
Solve: - 1 - 1
5X = 50 Check: 10 + 10 + 5 + 3(10) - 4 = 51
5 5 10 + 15 + 26 = 51
25 + 26 = 51
X = 10 51 = 51
Small: X = 10
Middle: 10 + 5 = 15
Large: 3(10) - 4 = 26
9. A
|
Type |
D |
R |
T |
|
Fast Boat |
12X |
X |
12 |
|
Slow Boat |
12(X-15) |
X |
12 |
|
Total |
600 |
|
|
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:
12X + 12(X - 15) = 600
Distributive Property: 12X + 12X -180 = 600
Combine Like Terms: 24X - 180 = 600
+180 +180
Solve for X: 24X = 780
24 24
X = 32.5
Substitute X into the chart and answer the question:
|
Type |
D |
R |
T |
|
Fast Boat |
12(32.5) =390 miles |
32.5 knots |
12 |
|
Slow Boat |
12(32.5-15) = 210 miles |
32.5-15 = 17.5 knots |
12 |
|
Total |
600 miles |
|
|
The answer from the chart is the slow boat traveled 210 miles.
________________________________________________________________________
10. UMMMMMMMMMMMMMMMMM!!!!!!! The answer is E!!!
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.