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.

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 $\displaystyle x$.

$\displaystyle \frac{3}{7}x=60$

$\displaystyle \frac{7}{3}(\frac{3}{7}x)=(60)\frac{7}{3}$

$\displaystyle x=\frac{60\cdot 7}{3}$

$\displaystyle x=\frac{420}{3}$

$\displaystyle x=140$

$\displaystyle \frac{3}{7}$ of $\displaystyle 140$ is $\displaystyle 60$, so $\displaystyle 140$ is the correct answer.