SOLVE WITH STEP BY STEP .
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.
2. 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:
3. The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
4. 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:
5. If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
Answers
1. 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.
2. Solution:
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 = 1.201.20
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 = 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.
3. 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 × 10¹² miles.
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 = 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 %
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.
5. Solution:
(0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (²/10) = 0.3010.
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 = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
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