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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.
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.
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
(a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost 10 cents, (e) gained 10 cents
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
4. The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
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
(a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 %
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 = Principal × Rate × Time
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.
6. Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
(a) three times as much, (b) twice as much, (c) the same, (d) half as much, (e) a third as much
Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
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.
7. If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
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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