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.

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

Let \(\displaystyle x\) be the number of actual miles. Then the proportion statement to be set up, with each ratio being number of actual miles to number of map inches, is:

\(\displaystyle \frac{60}{1\tfrac{1}{2}} = \frac{x}{N}\)

Simplify the left expression and solve for \(\displaystyle x\)

\(\displaystyle \frac{x}{N} = \frac{60}{1\tfrac{1}{2}} = 60 \div \frac{3}{2} =60 \cdot \frac{2}{3}\)

\(\displaystyle \frac{x}{N} = 40\)

\(\displaystyle x = 40N\)

$1 can be exchanged for 8 grotniks and 8 kronkheits, or, equivalently, 8.5 grotniks  (8 kronkheits is one-half of a grotnik). 100 gazoos is equal to \(\displaystyle 100 \cdot 12 = 1,200\) grotniks. Therefore, if \(\displaystyle D\) is the number of dollars that can be exchanged for the 100-gazoo bill, we can set up the proportion:

\(\displaystyle \frac{D}{1,200} = \frac{1}{8.5}\)

Solve for \(\displaystyle D\):

\(\displaystyle \frac{D}{1,200} \cdot 1,200 = \frac{1}{8.5}\cdot 1,200\)

\(\displaystyle D = \frac{1,200}{8.5} \approx 141.18\)

That is, the 100-gazoo bill can be exchanged for $141.18.