Question 10 on the MAT0020/24C Beginning Algebra State Exam
Solve a Word Problem
10. The length of a rectangle is 2 feet more than the width. The perimeter of the rectangle is 72 feet. Find the length.
A. 19 feet B. 17 feet C. 37 feet D. 35 feet
Solution:
The first step is to translate the statements into algebraic expressions.
The length of a rectangle is 2 feet more than the width would be represented by: x + 2
The width would be represented by: x
Here is a visual representation:
The next step is to create an algebraic equation to solve for x.
Since the perimeter is the sum of the sides, the equation would be:
(x) + (x + 2) + (x) + (x + 2) = 72
The next step is to combine like terms:
4x + 4 = 72
Then solve for x:
x = 17
Since x is the width, then the width is 17. The length is x + 2, so the length is 19.
The answer is 19.
Note: You can check your solution by substituting it back into your algebraic equation.
Practice Problems for Question 10
Solve a Word Problem
Solutions explained in following pages.
1. A CD is priced at $15.00, but it is on sale for 20% off. What is the sale price of the CD?
a. $3.00 b. $10.00 c. $18.00 d. $12.00
2. 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
3. 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
4. Find the simple interest percent if you invested $1000.00 for 5 years and you received $500.00 in interest.
a. 20% b. 50% c. 10% d. 40%
5. 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
6. 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
7. 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 c. 390 nautical miles
1. D
To find the discount you multiply the original price by the percent of the discount.
So, the discount is $15.00(0.20) = $3.00.
To find the sale price you subtract the original price from the discount.
So, to find the sale price you take 15.00 – 3.00 = 12.00. The sale price is $12.00.
________________________________________________________________________
2. 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
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3. B
Original Cost + Increase = New Price Check: 1083.33 + .20(1083.33) = 1300
X + .20X = 1300 1083.33 + 216.67 = 1300
1X + .20X = 1300
1300 = 1300
1.20X = 1300
1.20 1.20
X = $1083.33
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4. C
The formula to find simple interest is: Interest = Principal x Rate x Time (I = P*R*T)
The information gives would lead to: 500 = (1000)X (5)
Then simplify: 500 = X(5000)
Then solve for x by dividing both sides by 5000: 500/5000 = X(5000)/5000
X = 0.10, the simple interest percent would be 10%.
Check: 500 = 1000(0.10)(5)
500 = 500
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5. 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
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6. 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
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7. 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.