Math 50 (Elementary Algebra)
Test 2 : (Applications)
Name : ____________________ 1
* Write down your equation clearly and present your answers with appropriate units.
* You have to use the method used in chapter 4 to solve these problems.
* No credit will be given if you only guess an answer.
* You are allowed to use a scientific calculator. Cell phone or other electronic devices
are not allowed.
Number
1
2
3
4
5
6
7
8
9
10
11
Points
6
6
6
6
6
6
6
6
6
6
6
Total
66
Your score
Comments
Test 2:
Part I score = ____________
Part II score = ____________
Total score = ____________
Current approximated course grade = ________________
1
Spring 2011
2
(1) A drawer contains 41 cents and 7 cents stamps. The number of 41 cents stamps is
four less than three times the number of 7 cents stamps. The total value of all the
stamps is $4.86. How many 41 cents stamps are in the drawer?
Stamps
@41 cents
Number
Value in cents
= Total value
@7 cents
Total
Equation:
Present your answer in one sentence.
(2) The perimeter of a triangle is 35 ft. One side of the triangle is 2 ft longer than the
second side. The third side is 3 ft shorter than twice the second side. Find the length
of each side.
Define your variables.
The second side = x ft ( Use x to express the first side and the third side.)
The first side =
The third side =
Equation:
Your answer in one sentence.
(3) In a triangle, the first angle is 15º more than the second angle. The third angle is 10˚
less than three times the second angle. Find the measure of each angle.
Define your variables.
The second angle = xº ( Use x to express the first and the third angles.)
The first angle =
The third angle =
Equation:
Present your answer in one sentence.
3
(4) The sale price of a free-weight home gym is $372, which is 20% off the regular
price. Find the regular price. (Regular price – Discount = Sale price)
Equation:
Your answer in one sentence.
(5) The manager of a camera store uses a markup rate of 20 % . Find the cost of a
camera selling for $198. (C + M= S )
Equation:
Your answer in one sentence.
(6) Five times the second of three consecutive even integers is six less than twice the
sum of the first and third integers. Find the middle even integer.
Define your variables.
The first even integer = n (Use n to express the second and the third numbers.)
The second even integer =
The third even integer =
Equation:
Your answer in one sentence.
(7) A television selling for $1260 has a markup of $320. Find the markup rate.
(Round your answer to the nearest percent.)
Set up an equation and solve the problem.
(8) The total value of the dimes and quarters in a bank is $6.05 There are six more
quarters than dimes. Find the number of each type of coin in the bank.
Coin
Dimes
Quarters
Number
Total
Set up an equation and solve the problem.
Value
10
25
Total Value
4
(9) In an isosceles triangle, one angle is 16º less than twice the measure of one of the
equal angles. Find the measure of each angle.
Equation:
Your answer in one sentence.
(10) The width of the rectangular foundation of a building is 30% of the length. The
perimeter of the foundation is 338 ft. Find the length and width of the
foundation.
Equation:
Your answer in one sentence.
(11) A 20-foot board is cut into two pieces. Twice the length of the shorter piece is 4 feet
more than the length of the longer piece. Find the length of the longer piece.
Define the variables:
L = the length of the longer piece
The length of the shorter piece = _________________
Set up the equation and solve the problem.
5
Math 50: Test 2
Part II:
♦ You must use the method we studied in chapter 4 to do these problems.
♦ Present your answer with appropriate units.
♦ Circle your answers.
Name : _________________
Part II(66) = ___________
Number
12
13
14
15
16
17
18
19
20
21
22
Points
6
6
6
6
6
6
6
6
6
6
6
Total
66
Your score
Comment
6
12. A bus traveling at a rate of 60 mph overtakes a car traveling at a rate of
45 mph. If the car had a 1.5-hour head start, how far from the starting point
does the bus overtake the car?
Rate
60mph
45mph
Bus
Car
Time
Distance
Equation:
Your answer in one sentence.
13. Company A rents cars for $25 per day and 8 cents per mile driven. Company B
rents cars for $15 per day and 14 cents per mile driven. You want to rent a car for
one week. Find the maximum number of miles(as a whole number) you can drive
a Company B car if it is to cost you less than a Company A car.
Let x be the number of miles driven in one week.
Use x to express the cost of company A and the cost of company B.
Cost for company A: _________________________________
Cost for company B: _________________________________
Inequality:
Your answer.
14. Two small planes start from the same point and fly in opposite directions. The
first plane is flying 40 mph slower than the second plane. In 3 hours the planes
are 1920 miles apart. Find the rate of the faster plane.
Rate
First plane
Second plane
Total
Set up an equation and present your answer.
Time
Distance
7
15. A rectangle is 8 ft wide and 2 x  3 ft long. Express as an integer the minimum
length, in feet, of the rectangle when the area is greater than 208 ft 2 .
( The area of a rectangle is equal to its length times its width.)
Set up an Inequality and present your answer.
16. A student’s grades on five math exams were 68, 82, 90, 73, and 95. Each exam
has maximum 100 points. In order to receive a B, the student must get 80% or
better. What scores on the sixth test will enable this student to receive a B in the
math course? ( Describe all possible scores.)
Set up an inequality and solve the problem
17. How many ounces of water evaporated from 60 oz of a 12% salt solution to
produce a 16% salt solution? (Hint: water has no salt.)
Amount Percent
= Quantity (pure salt)
Water
12%
16%
Set up an equation and present your answer.
8
18. A total of $9500 is deposited into simple interest accounts. On one account the
annual simple interest rates is 10%; on the second account the annual simple
interest is 11%. How much should be invested in the 11% account so that
the total annual interest earned is $1005?
Principal
Rate
= Interest
@10%
@11%
Total
Set up an equation and present your answwer:
19.
How many gallons of a 15% acid solution and 20% acid solution must be
mixed to make a 20 gallons of 16% acid solution?
Solution
15% acid
Amount
Percent
Quantity (pure acid)
20% acid
16% acid
Equation and your answer:
20. A bicycling club rides out into the country at a speed of 15 mph and returns
over the same road at 12 mph. How far does the club ride out into the country
if it travels a total of 9 hours?
Rate
To the country
Return home
Time
Distance
9
21. An investment counselor for a corporation invested 70% of the company’s
investment account in 6.54% short-term certificates. The remainder was
invested in 6% corporate bonds. The annual interest earned from the two
investments was $1913.40. How much money was invested in each account?
Principal
Rate
Interest
@6.54%
@6%
Total
Set up an equation and present your answer.
22.
How many pounds of walnuts that cost $2 per pound must be mixed
with 20 lb of cashews that cost $5 per pound to make a mixture that sells
for $2.75 per pound?
Amount
Unit Cost
$2 walnuts
$5 cashews
$2.75 mixture
Set up an equation and present your answer.
Value