MTH208 Week 5 Final Exam Solution Key
I. True or False (5 Points)

The opposite number of positive 3 is negative 3 True

Negative 6 is greater than negative 3 False

To isolate t in 2t = 7 + t, subtract “t” from each side True

The solution to 2x – 3 = x + 1 is 4 True

If x is no larger than 8, then x £ 8 True

3 < 8 and 3 > 1 True

The point (2, 4) satisfies the equation 2y – 3x = 8 False

The line y = x has no y intercept False

The equations y = 2x + 7 and y = 2x + 8 are inconsistent True

We can eliminate either variable by using the addition method True
II. Solve the following (20 Points)


Build up fraction ¾ =?/20 15/20

Reduce fraction to lowest terms 84/60 21/15

Perform the indicated operation

13 – (7) = 20

–(1/3) + (3/5) = 4/15

Evaluate each expression

3 [(2 – 3)2 + (6 – 4)2] = 15

42 – 4 (1) (3) = 28

The US population is onefourth China’s population. If the US has 300 million people, then what is the population of China
The population of China is 1.2 Billion.

If a rectangular patio has a length that is 3 feet longer than its width and a perimeter of 42 feet, then the width can be found by solving the equation 2x + 2 (x + 3) = 42. What is the width?
The width of the patio is 9 feet.

Solve the following equation by eliminating fractions

X/2 + X/3 = 20 X = 24

3m/4 + m/2 =  5 m = 4

Solve x + 4y = 12 for y. Write the answer in the form y = mx + c, where m and c are fixed real numbers
y = 1/4x + 3

Translate each verbal expression into an algebraic expression

Five subtracted from a number
x – 5

The ratio of a number and six
x / 6

If the perimeter of a tennis court is 228 feet and the length is 6 feet longer than twice the width, then what are the length and width?
Length = 98 feet
Width = 46 feet

Solve for the indicated variable

m = aPw for a
a = (m+w)/P

2x – 3 = ax for x
x = 3/(2a)

Identify the variable and write an inequality

Tony is taller than 6 feet
X > 6 feet (Tony = X)

The minimum speed of the freeway is 45 mph
X ≥ 45 mph ( Speed = X)

Brandon gets 40% discount on loose diamonds where he works. The cost of the setting is $250. If he plans to spend at most $1450, then what is the price range (list price) of the diamonds that he can afford?
Brandon can afford list price diamonds up to $2000.

Define

Origin
The origin is the point where the xaxis and yaxis intersect. The origin should be (0,0).

Intercepts
An intercept is the point where a graph crosses the xaxis or y axis. This crossing point is called the xintercept or the y intercept.

Solve the following system by the addition method
0.05x + 0.10y = 1.3 and
x + y = 19
(10) .05x + .1y = 1.3 (10)
.5x  y = 13
x + y = 19
.5x = 6
x = 12
12 + y = 19
y = 7
(12, 7)

Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?
206 Adult Tickets Sold
103 Student Tickets Sold
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