If a number is increased by 37%, by what percent must it be decreased to obtain the original number?
A carpeted living room and dining room area measures 32 ft by 10 ft. Mark decides to install wood flooring in the 12 ft by 10 ft dining room. By what percent has he reduced the area that is carpeted?
Planets A, B, and C orbit a certain star once every 3, 5, and 18 months, respectively. If the three planets are now in the same straight line, what is the smallest number of months that must pass before they line up again?
Rob can complete his bus route in 6 hours. Joan can complete her bus route in 3 hours. If they left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leavae the terminal at the same time.
Cluless,
If you remain clueless, you will not pass your exam. We like to see you put in some efforts. I will solve the first one for you, and expect you to show some of your work for the rest.
MathMate
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Let the original number be 100.
After increasing by 37%, it becomes
100(1+0.37)=137
To get back to 100, we need to multiply by
137*(100/137)
So the percentage to reduce is
1-100/137=37/137 (convert to %).
The answer would be 27.01%
Hello and thanks for your help. I am not completly dazed. I have 40 questions and these were the ones that I just could not get right. I appreciate efforts and time.
Correct for the 1st one.
For the second, since the width is the same, you can calculate the percentage decrease in the length.
The third one has to do with LCM.
I came up with 90 months for the second one.
The third one would be 9:00 am.
THANKS !
To find the percent decrease needed to obtain the original number after increasing it by 37%, you can follow these steps:
1. Start with the original number, let's call it "X."
2. Increase X by 37%, which means adding 37% of X to X. This can be calculated by multiplying X by 1.37.
New Value = X + 1.37X = 2.37X
3. Now, you want to decrease the new value back to the original value, X.
4. Let's calculate the difference between the new value (2.37X) and the original value (X):
Difference = 2.37X - X = 1.37X
5. To find the percentage decrease, divide the difference by the new value and multiply by 100:
Percentage Decrease = (Difference / New Value) * 100 = (1.37X / 2.37X) * 100 ≈ 57.82%
Therefore, you would need to decrease the number by approximately 57.82% to obtain the original number.
Now let's move on to the next question.
To determine the percentage by which Mark has reduced the area that is carpeted, follow these steps:
1. Calculate the original area of the living room and dining room, which is 32 ft x 10 ft = 320 sq ft.
2. Calculate the area of the dining room with wood flooring, which is 12 ft x 10 ft = 120 sq ft.
3. Subtract the area with wood flooring (120 sq ft) from the original area (320 sq ft) to find the reduced area:
Reduced Area = 320 sq ft - 120 sq ft = 200 sq ft.
4. To find the percentage reduction, divide the reduced area by the original area and multiply by 100:
Percentage Reduction = (Reduced Area / Original Area) * 100 = (200 sq ft / 320 sq ft) * 100 ≈ 62.5%
Mark has reduced the carpeted area by approximately 62.5%.
Let's move on to the next question.
To determine the smallest number of months that must pass before the three planets line up again, we need to find the least common multiple (LCM) of their orbital periods.
1. The orbital periods of the three planets are 3 months, 5 months, and 18 months, respectively.
2. Find the LCM of these three numbers.
To find the LCM, we can break down the numbers into their prime factorization:
3 = 3
5 = 5
18 = 2 * 3 * 3
Then we take each prime factor to its highest power:
2^1 * 3^2 * 5^1 = 90
Therefore, the LCM of the orbital periods is 90 months. It will take 90 months for the three planets to line up again.
Now, onto the final question.
To determine the next time Rob and Joan would leave the terminal at the same time, we need to find the least common multiple (LCM) of their bus route completion times.
1. Rob completes his bus route in 6 hours.
2. Joan completes her bus route in 3 hours.
3. Find the LCM of 6 and 3.
To find the LCM, we can note that 6 and 3 have a common prime factor, which is 3. Since 3 is the only common prime factor, we multiply the two numbers:
6 * 3 = 18
Therefore, the LCM of their completion times is 18 hours.
Since they left the terminal at 3:00 am and the LCM is 18, they will leave the terminal at the same time again 18 hours later.
3:00 am + 18 hours = 9:00 pm
So, the next time they will leave the terminal at the same time is 9:00 pm.