Solve Arithmetic Word Problems - Air Force Officer Qualifying Test AFOQT

1. At $60\ \text{mph}$, how long does it take to travel $90$ miles?

   $1.5\ \text{hours}$. Divide the distance by the speed to determine the time required.

2. A car travels $150$ miles in $3$ hours. What is its average speed?

   $50\ \text{mph}$. Divide the total distance by the total time to calculate average speed.

3. What is $15\%$ of $200$?

   $30$. Multiply the whole by the decimal form of the percentage to find the part.

4. Two machines make parts at $6$ and $4$ parts/min. What is the combined rate?

   $10\ \text{parts/min}$. Sum the individual rates to obtain the combined production rate.

5. A worker earns $18/hour for $8$ hours plus a $45 bonus. What is total pay?

   $189. Multiply the hourly rate by hours worked and add the bonus for total earnings.

6. What percent is equivalent to the decimal $0.08$?

   $8\%$. Convert a decimal to a percentage by multiplying by $100$.

7. State the percent equation relating part, whole, and percent.

   $\text{part}=\text{percent}\times\text{whole}$. This equation calculates the part by multiplying the percentage (in decimal form) by the whole.

8. A solution is $10\%$ salt by mass. How much salt is in $250$ g of solution?

   $25\ \text{g}$. Multiply the total solution mass by the decimal equivalent of the salt percentage.

9. If $\frac{3}{5}$ of a number is $24$, what is the number?

   $40$. Divide the given part by the fraction to solve for the whole number.

10. A recipe uses a ratio of $2:3$ (oil:vinegar). If vinegar is $12$ oz, how much oil?

    $8\ \text{oz}$. Use the ratio to set up a proportion and solve for the oil amount based on vinegar.

11. A tank drains at $2$ gal/min from $50$ gal. How much remains after $10$ minutes?

    $30\ \text{gal}$. Subtract the drained amount, rate times time, from the initial volume.

12. What decimal is equivalent to $35\%$?

    $0.35$. Convert a percentage to a decimal by dividing by $100$.

13. A runner completes $5$ miles in $40$ minutes. What is the pace in minutes per mile?

    $8\ \text{min/mi}$. Divide the total time by the distance to find the pace per mile.

14. A value decreases from $60$ to $45$. What is the percent decrease?

    $25\%$. Divide the decrease by the original value and multiply by $100$ to find the percentage.

15. A store discounts an item $20\%$ off $50$. What is the sale price?

    $40$. Subtract the discount, calculated as the percentage of the original price, from the original.

16. After a $10\%$ tax, a $30$ item costs what total amount?

    $33$. Add the tax, found by multiplying the price by the tax rate, to the original price.

17. If $x$ is increased by $12\%$, what is the resulting expression in terms of $x$?

    $1.12x$. Add $1$ to the decimal form of the percentage and multiply by $x$ for the increased value.

18. State the rate formula used in word problems (distance, rate, and time).

    $d=rt$. The formula expresses distance as the product of rate and time in arithmetic word problems.

19. A price increases from $80$ to $100$. What is the percent increase?

    $25\%$. Divide the increase by the original amount and multiply by $100$ to find the percentage.

20. A map scale is $1$ inch : $20$ miles. What distance is $3.5$ inches?

    $70\ \text{miles}$. Multiply the map measurement by the scale ratio to find the actual distance.

21. In a group with ratio men:women $3:5$, there are $40$ people. How many men?

    $15$. Determine the fraction of men from the ratio and multiply by total people.

22. A mixture is $30\%$ acid. How many liters of acid are in $20$ liters of mixture?

    $6\ \text{L}$. Multiply the total mixture volume by the decimal form of the acid percentage.

23. A tank fills at $3$ gal/min. How many gallons fill in $12$ minutes?

    $36\ \text{gal}$. Multiply the filling rate by the time to calculate the total volume filled.

24. State the proportion rule for equivalent ratios $\frac{a}{b}=\frac{c}{d}$.

    $ad=bc$. Cross-multiplying the ratios yields the condition for their equivalence.

25. What fraction in simplest form is equivalent to $25\%$?

    $\frac{1}{4}$. Convert the percentage to a fraction by dividing by $100$ and simplifying.

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