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**1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.**

**Solution:**

Let the 1st paycheck be x (integer).

Mrs. Rodger got a weekly raise of $ 145.

So after completing the 1st week she will get $ (x+145).

Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.

= $ (x + 145 + 145)

= $ (x + 290)

So in this way end of every week her salary will increase by $ 145.

(a) 10, (b) 16, (c) 18, (d) 36, (e) 64

Solution:

x + x(x

Put the value of x = 2 in the above expression we get,

2 + 2(2

= 2 + 2(2 × 2)

= 2 + 2(4)

= 2 + 8

= 10

**3. Mr. Jones sold two pipes at $1.20 each. Based on the cost, his
profit one was 20% and his loss on the other was 20%. On the sale of the
pipes, he:
(a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost 10 cents, (e) gained 10 cents
**

Selling price of the first pipe = $1.20

Profit = 20%

Let’s try to find the cost price of the first pipe

CP = Selling price - Profit

CP = 1.20 - 20% of CP

CP = 1.20 - 0.20CP

CP + 0.20CP = 1.20

1.20CP = 1.20

CP = \(\frac{1.20}{1.20}\)

CP = $ 1

Selling price of the Second pipe = $1.20

Loss = 20%

Let’s try to find the cost price of the second pipe

CP = Selling price + Loss

CP = 1.20 + 20% of CP

CP = 1.20 + 0.20CP

CP - 0.20CP = 1.20

0.80CP = 1.20

CP = \(\frac{1.20}{0.80}\)

CP = $1.50

Therefore, total cost price of the two pipes = $1.00 + $1.50 = $2.50

And total selling price of the two pipes = $1.20 + $1.20 = $2.40

Loss = $2.50 – $2.40 = $0.10

Therefore, Mr. Jones loss 10 cents.

**Answer:** ** ****(d) **

(a) 587 × 10

Solution:

The distance of the light travels in 100 years is:

5,870,000,000,000 × 100 miles.

= 587,000,000,000,000 miles.

= 587 × 10

**5. A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500
at 4 %. In order to have a yearly income of $ 500, he must invest the
remainder at:
(a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 %
Solution:**

Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.

= $ 4000 × 5/100.

= $ 4000 × 0.05.

= $ 200.

Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.

= $ 3500 × 4/100.

= $ 3500 × 0.04.

= $ 140.

Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.

Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.

= $ 160.

Total invested amount = $ 4000 + $ 3500 = $7500.

Remaining invest amount = $ 10000 - $ 7500 = $ 2500.

We know that,

Interest = $ 160,

Principal = $ 2500,

Rate = r [we need to find the value of r],

Time = 1 year.

160 = 2500 × r × 1.

160 = 2500r

160/2500 = 2500r/2500 [divide both sides by 2500]

0.064 = r

r = 0.064

Change it to a percent by moving the decimal to the right two places r = 6.4 %

Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.

(a) three times as much, (b) twice as much, (c) the same, (d) half as much, (e) a third as much

Solution:

Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.

We know that

Or,

So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.

And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.

= 100/x hr.

So we can clearly see that his new time compared with the old time was: twice as much.

(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0

Solution:

(0.2)

Taking log on both sides

log (0.2)

x log (0.2) = 0.3010, [since log 2 = 0.3010].

x log (

x [log 2 - log 10] = 0.3010.

x [log 2 - 1] = 0.3010,[since log 10=1].

x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].

x[-0.699] = 0.3010.

x =

x = -0.4306….

x = -0.4 (nearest tenth)

(a)

Solution:

10

(10

10

10

(a) 5x, -11, (b) -11, 5x, (c) -1, 3, (d) 3, -1, (e) 5, -11

Solution:

(a) 15, (b) 20, (c) 30, (d) 32, (e) 33

Solution:

Let the three numbers be x, y and z.

Sum of the numbers is 98.

x + y + z = 98………………(i)

The ratio of the first to the second is

x/y =

x =

x =

The ratio of the second to the third is

z =

z =

Put the value of x =

49y = 98 × 15.

49y = 1470.

y =

y = 30 .

Therefore, the second number is 30.

Unsolved Questions:

**1.** Fahrenheit temperature F is a linear function of Celsius
temperature C. The ordered pair (0, 32) is an ordered pair of this
function because 0°C is equivalent to 32°F, the freezing point of water.
The ordered pair (100, 212) is also an ordered pair of this function
because 100°C is equivalent to 212° F, the boiling point of water.

**2.** A sports field is 300 feet long. Write a formula that gives the
length of x sports fields in feet. Then use this formula to determine
the number of sports fields in 720 feet.

**3.** A recipe calls for 2 1/2 cups and I want to make 1 1/2 recipes. How many cups do I need?

**4.** Mario answered 30% of the questions correctly. The test
contained a total of 80 questions. How many questions did Mario answer
correctly?

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