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HiSET: Math : Multi-step real-world and mathematical problems

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Example Questions

Example Question #1 : Multi Step Real World And Mathematical Problems

An electronics store is having a sale and offering $25\%$ $\displaystyle 25\%$ off the regular prices of all laptop computers. If the sale price for a certain laptop is $\$450.00$ $\displaystyle \$450.00$, what is the regular price of the laptop?

Possible Answers:

$\$1800.00$ $\displaystyle \$1800.00$

$\$150.00$ $\displaystyle \$150.00$

$\$600.00$ $\displaystyle \$600.00$

$\$300.00$ $\displaystyle \$300.00$

$\$900.00$ $\displaystyle \$900.00$

Correct answer:

$\$600.00$ $\displaystyle \$600.00$

Explanation:

Notice that $\$450.00$ $\displaystyle \$450.00$ is the price after the $25\%$ $\displaystyle 25\%$ discount. Therefore, the sale price of $\$450.00$ $\displaystyle \$450.00$ is $75\%$ $\displaystyle 75\%$ of the regular price (or 0.75 $\displaystyle 0.75$ times the regular price). The regular price can be represented as $100\%$ $\displaystyle 100\%$, or $\displaystyle 1$ times the regular price.

First, set up a proportion describing the problem, using $\displaystyle x$ to represent the unknown quantity, the regular price:

$\frac{\$450.00}{0.75} = \frac{x}{1}$ $\displaystyle \frac{\$450.00}{0.75} = \frac{x}{1}$

Next, cross multiply:

$\$450.00\cdot 1= 0.75\cdot x$ $\displaystyle \$450.00\cdot 1= 0.75\cdot x$

Finally, divide both sides by 0.75 $\displaystyle 0.75$ to solve for $\displaystyle x$:

$x=\frac{\$450.00}{0.75}$ $\displaystyle x=\frac{\$450.00}{0.75}$

$x=\$600$ $\displaystyle x=\$600$

Therefore, the regular price is $\$600.00$ $\displaystyle \$600.00$.

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Example Question #2 : Multi Step Real World And Mathematical Problems

3 sticks of butter weigh 12 ounces combined. Using this information, determine the weight of 7 sticks of butter.

Possible Answers:

$84\; ounces$ $\displaystyle 84\; ounces$

$28\; ounces$ $\displaystyle 28\; ounces$

$16\; ounces$ $\displaystyle 16\; ounces$

$32\; ounces$ $\displaystyle 32\; ounces$

$4\; ounces$ $\displaystyle 4\; ounces$

Correct answer:

$28\; ounces$ $\displaystyle 28\; ounces$

Explanation:

Set up a proportional relationship, using $\displaystyle x$ to represent the unknown quantity (the weight of 7 sticks of butter):

$\frac{12\ ounces}{3\ sticks} = \frac{x\ ounces}{7\ sticks}$ $\displaystyle \frac{12\ ounces}{3\ sticks} = \frac{x\ ounces}{7\ sticks}$

Cross multiply:

$12\cdot 7 = 3\cdot x$ $\displaystyle 12\cdot 7 = 3\cdot x$

$84 = 3\cdot x$ $\displaystyle 84 = 3\cdot x$

Finally, divide both sides to solve for $\displaystyle x$:

$\frac{84}{3} = x$ $\displaystyle \frac{84}{3} = x$

$x = 28\ ounces$ $\displaystyle x = 28\ ounces$

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Example Question #1 : Proportional Relationships

If $\displaystyle A$ is inversely related to $\displaystyle B$ and $\displaystyle C$ and $\displaystyle A$ is directly related to $\displaystyle Z$, which formula describes the relationship between A,B,C, $\displaystyle A,B,C,$ and $\displaystyle Z$?

Possible Answers:

$A = \frac{Z}{BC}$ $\displaystyle A = \frac{Z}{BC}$

$A = \frac{BC}{Z}$ $\displaystyle A = \frac{BC}{Z}$

$A = \frac{B}{Z}+ \frac{C}{Z}$ $\displaystyle A = \frac{B}{Z}+ \frac{C}{Z}$

$A = \frac{1}{Z}+BC$ $\displaystyle A = \frac{1}{Z}+BC$

$A = \frac{1}{BC}+Z$ $\displaystyle A = \frac{1}{BC}+Z$

Correct answer:

$A = \frac{Z}{BC}$ $\displaystyle A = \frac{Z}{BC}$

Explanation:

To say that $\displaystyle x$ is inversely related to $\displaystyle y$ is to say $x=\frac{1}{y}$ $\displaystyle x=\frac{1}{y}$.

To say that $\displaystyle x$ is directly related to $\displaystyle y$ is to say x=y $\displaystyle x=y$.

Thus, to say $\displaystyle A$ is inversely related to $\displaystyle B$ and $\displaystyle C$ and $\displaystyle A$ is directly related to $\displaystyle Z$ is to say

$A=\frac{Z}{BC}$ $\displaystyle A=\frac{Z}{BC}$

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HiSET: Math : Multi-step real-world and mathematical problems

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #1 : Multi Step Real World And Mathematical Problems

Example Question #2 : Multi Step Real World And Mathematical Problems

Example Question #1 : Proportional Relationships

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