\(\displaystyle 20\%\textup{ of }\) \(\displaystyle \frac{4}{5}\) is equal to

\(\displaystyle \frac{20}{100} \cdot \frac{4}{5} = \frac{80}{500} = \frac{80 \div 20 }{500 \div 20} = \frac{4}{25}\)

Let \(\displaystyle N\) be the number in question. \(\displaystyle 20\%\) of this number is equal to \(\displaystyle \frac{4}{5}\), so

\(\displaystyle \frac{20}{100} \cdot N = \frac{4}{5}\)

\(\displaystyle \frac{100} {20} \cdot \frac{20}{100} \cdot N =\frac{100} {20} \cdot \frac{4}{5}\)

\(\displaystyle N =\frac{400} {100} = 4\)

Jill buys a new tablet for \(\displaystyle \$156.45\). If she used a coupon and received \(\displaystyle \$35\) off of the original price, what was the percent discount she received?

So, to find percent discount, we need to calculate the original price. 

\(\displaystyle 156.45+35=191.45\)

Then, we need to find the percent of the discount. To do so, simply divide the amount of the discount by the original amount, then multiply by 100

\(\displaystyle \frac{35}{191.45}*100=18.3\%\)

Here, we need to first convert the percent into a fraction. Then, we will solve the equation. \(\displaystyle 12\%=\frac{12}{100}.\) Our number is unknown, so I will call it \(\displaystyle x.\)

\(\displaystyle \frac{12x}{100}=138.\)  \(\displaystyle x=\frac{138*100}{12}=1150.\)

All three are equal.

30% of 40% of 50% of \(\displaystyle x\) is \(\displaystyle \frac{3}{10}\) of \(\displaystyle \frac{2}{5}\) of \(\displaystyle \frac{1}{2}\) of \(\displaystyle x\): that is, \(\displaystyle \frac{3}{10} \cdot\frac{2}{5}\cdot\frac{1}{2} \cdot x = \frac{6}{100} x\)

40% of 50% of 30% of \(\displaystyle x\) is \(\displaystyle \frac{2}{5}\) of \(\displaystyle \frac{1}{2}\) of \(\displaystyle \frac{3}{10}\) of \(\displaystyle x\): that is, \(\displaystyle \frac {2}{5} \cdot\frac{1}{2} \cdot\ \frac{3}{10} \cdot x = \frac{6}{100} x\)

 50% of 30% of 40% of \(\displaystyle x\) is \(\displaystyle \frac{1}{2}\) of \(\displaystyle \frac{3}{10}\) of \(\displaystyle \frac{2}{5}\) of \(\displaystyle x\): that is \(\displaystyle \frac{1}{2} \cdot\ \frac{3}{10} \cdot \frac {2}{5} \cdot x = \frac{6}{100} x\)

The ratio \(\displaystyle \dpi{100} \small 4\) to \(\displaystyle \frac{1}{4}\) is equal to \(\displaystyle \frac{4}{\frac{1}{4}}\) which is  \(\displaystyle 4\left ( \frac{4}{1} \right )= 16\).

\(\displaystyle \dpi{100} \small 16\) can be written as the ratio \(\displaystyle \dpi{100} \small 16\) to \(\displaystyle \dpi{100} \small 1\).

The monthly budget is found by:

\(\displaystyle \frac{25,200}{12}=2,100\)

which for 3 months is a budget of:

\(\displaystyle 2,100\cdot 3= 6,300\)

To find out how much they are over budget the budgeted amount is subtracted from the actual expenses.
\(\displaystyle 7,420 - 6,300 = 1,120\)

The ratio \(\displaystyle \dpi{100} \small 3\) to \(\displaystyle \dpi{100} \small \frac{1}{2}\) is the same as \(\displaystyle \dpi{100} \small \frac{3}{\frac{1}{2}}=3\times \frac{2}{1}=6\),
which equals a ratio of \(\displaystyle \dpi{100} \small 6\) to \(\displaystyle \dpi{100} \small 1\).

Also, if you double both sides of the ratio, you get \(\displaystyle \dpi{100} \small 6\) to \(\displaystyle \dpi{100} \small 1\). 

\(\displaystyle 7x + 5x+4x= 64\)

\(\displaystyle 16x=64\)

\(\displaystyle x=4\)

bracelets: \(\displaystyle 5x=5(4)=20\)

If \(\displaystyle \frac{1}{3}\) are red, then \(\displaystyle \frac{2}{3}\) are blue, and the number of blue marbles can be written as

\(\displaystyle blue=\frac{2}{3}*total marbles\)

Plug in the number of blue marbles, 30, and solve for the total marbles.

\(\displaystyle 30 = \frac{2}{3}*total\rightarrow total = \frac{30}{\frac{2}{3}} =45 marbles\)