The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.

If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90y = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.

Similarly, we can write 15% of x as 0.15x = (15/100)x = (3/20)x.

Now, we set these two expressions equal to one another.

(9/10)y = (3/20)x

Multiply both sides by 20 to eliminate fractions.

18y = 3x

The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.

18y = 3x

Divide both sides by 3.

6y = x

Divide both sides by y.

6 = x/y

Thus, the ratio of x to y is 6.

The answer is 6.

First convert the percentage to a decimal:

7.5% = .075

Then turn this into a fraction:

.075 = 75/1000

Simplify by dividing the numerator and denominator by 25:

75/1000 = 3/40

25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)

To convert a percent into a fraction, simply divide by 100 and reduce. In our case, 62 and 100 have the common factor of 2, so solving and simplification are as follows:

$\displaystyle \frac{62}{100}\rightarrow \frac{31}{50}$

Convert the improper fraction $\displaystyle \frac{7}{5}$ to the mixed numeral $\displaystyle 1\frac{2}{5}$ or as the decimal $\displaystyle 1.4$.  $\displaystyle 1.4$ as a percentage is $\displaystyle 140\%$

First, we will determine the total number of ballots:

$\displaystyle 4+4+5+7+12+13=45\hspace{1 mm}ballots$

Since there are two four year olds, and this question is asking the probability of the chosen child being four, the probability is:

$\displaystyle \frac{4+4}{45}=\frac{8}{45}=0.1\overline{7}=17.\overline{7}\%$

The first hen lays 8 brown eggs: 2/5 * 20 = 8

The second lays 5 brown eggs: 1/4 * 20 = 5

The third lays 6 brown eggs: 3/10 * 20 = 6

Add up the brown eggs and divide by 60, the total number of eggs:

19/60 = 0.31666667 = 31.67%, or 32%.

We can right 23% as a fraction and set that equal to $\displaystyle x$ over the original price. 

$\displaystyle \frac{23}{100}=\frac{x}{18.59}$

From here we cross multiply and divide.

$\displaystyle \frac{23 * 18.59}{100}= 4.2757$

We round this number to $4.28. This is the amount of discoount we need to apply to the original price. To do this we subtract 4.28 from 18.59.

$\displaystyle \$18.59-\$4.28=\$14.31$

The goal of this problem is to solve for how much Louisa and Caroline have saved, together, towards their goal money for starting a small business.  In order to do that, you must add what Louisa has saved to what Caroline has saved, then convert the fraction into a percentage.

Add Louisa and Caroline:

$\displaystyle \frac{4}{9} + \frac{2}{6}$

Find the lowest common multiple for the denominator:

$\displaystyle \frac{8}{18} + \frac{6}{18}$

Add:

$\displaystyle \frac{14}{18}$

Simplify:

$\displaystyle \frac{7}{9}$

To convert a fraction into a percentage, simply multiply the numerator by 100 and divide by the denominator. There are other methods, but this is the easiest.

$\displaystyle \frac{7\cdot 100}{9}$

Equals

$\displaystyle 77.78% \approx 78%$$\displaystyle 77.78 \approx 78$

78% is your answer.

6 students achieved a score of 201-300; 18 achieved a score of 301-400; 30 achieved a score of 401-500. Add these:

$\displaystyle 6 + 18 + 30 = 54$

The number of students who took the test is the sum of the students who finished in the six ranges:

$\displaystyle 6 + 18 + 30 + 40 + 16 + 10 = 120$

The question is now to find out what percent 54 is of 120, which can be calculated as follows:

$\displaystyle \frac{54}{120} \times 100 \% = 45 \%$