Rewrite the expression using a division sign.

\(\displaystyle \frac{\frac{1}{2}}{2}+\frac{2}{\frac{1}{2}}=\frac{1}{2}\div2+2 \div \frac{1}{2}\)

Take the reciprocal of the term after the division signs and convert the division sign to a multiplication sign.

\(\displaystyle \frac{1}{2}\times\frac{1}{2}+2 \times2=\frac{1}{4}+4=4\frac{1}{4}=\frac{17}{4}\)

Let \(\displaystyle x\) be the cost of the car before the discount. Since we know that the car at a discount costs \(\displaystyle \$6,000\), we can write the following equation:

\(\displaystyle x-0.25x=6000\)

Now, solve for \(\displaystyle x\) to find the cost of the car before the discount.

\(\displaystyle 0.75x=6000\)

\(\displaystyle x=\frac{6000}{0.75}\)

\(\displaystyle x=8000\)

The car originally cost \(\displaystyle \$8,000\) before the \(\displaystyle 25\%\) discount was applied.

Let \(\displaystyle x\) be the total number of marbles in the bag. Since we know that \(\displaystyle 12.5\%\) of the marbles are yellow, we can set up the following equation and solve for \(\displaystyle x\):

\(\displaystyle 0.125x=10\)

\(\displaystyle x=\frac{10}{0.125}\)

\(\displaystyle x=80\)

There are \(\displaystyle 80\) total marbles in the bag.

Let \(\displaystyle x\) be the total number of calories Byron eats in a day. With the information given in the question, we can write the following equation and solve for \(\displaystyle x\).

\(\displaystyle 0.25x=600\)

\(\displaystyle x=\frac{600}{0.25}\)

\(\displaystyle x=2400\)

Byron eats \(\displaystyle 2400\) calories for the day described in the question.

Let \(\displaystyle x\) be the cost of the t-shirt before it went on sale. With the information given in the question, we can write the following equation and solve for \(\displaystyle x\).

\(\displaystyle x-0.15x=15\)

This can be rewritten as:

\(\displaystyle 1x-0.15x=15\)

\(\displaystyle 0.85x=15\)

\(\displaystyle x=\frac{15}{0.85}\)

\(\displaystyle x=17.65\)

The shirt cost \(\displaystyle \$17.65\) before the sale.

Let \(\displaystyle x\) be the cost of the vacuum before the sale. With the information given in the question, we can write the following equation and solve for \(\displaystyle x\).

\(\displaystyle x-0.18x=20.25\)

This can be rewritten as:

\(\displaystyle 1x-0.18x=20.25\)

\(\displaystyle 0.82x=20.25\)

\(\displaystyle x=\frac{20.25}{0.82}\)

\(\displaystyle x=24.70\)

The vacuum cost \(\displaystyle \$24.70\) before it went on sale.

Let \(\displaystyle x\) be the price of the non-discounted ticket. With the information given in the question, we can write the following equation and solve for \(\displaystyle x\).

\(\displaystyle x-0.35x=850\)

\(\displaystyle 0.65x=850\)

\(\displaystyle x=\frac{850}{0.65}\)

\(\displaystyle x=1307.69\)

The plane ticket that Teresa bought would have cost \(\displaystyle \$1307.69\) if it were not on sale.

Let \(\displaystyle x\) be the total number of marbles in the bag. With the information given in the question, we can write the following equation and solve for \(\displaystyle x\).

\(\displaystyle 0.75x=12\)

\(\displaystyle x=\frac{12}{0.75}\)

\(\displaystyle x=16\)

There are \(\displaystyle 16\) total marbles in the bag.

Let \(\displaystyle x\) be the number we are looking for. With the information given in the question, we can write the following equation and solve for \(\displaystyle x\).

\(\displaystyle 0.125x=112\)

\(\displaystyle x=\frac{112}{0.125}\)

\(\displaystyle x=896\)

\(\displaystyle 12.5\%\) of \(\displaystyle 896\) is \(\displaystyle 112\), so \(\displaystyle 896\) is the correct answer.

Let \(\displaystyle x\) be the number we are looking for. With the information given in the question, we can write the following equation and solve for \(\displaystyle x\).

\(\displaystyle \frac{1}{5}x=50\)

\(\displaystyle \frac{5}{1}(\frac{1}{5}x)=(50)\frac{5}{1}\)

\(\displaystyle x=250\)

\(\displaystyle \frac{1}{5}\) of \(\displaystyle 250\) is \(\displaystyle 50\), so \(\displaystyle 250\) is the correct answer.