Solve Algebra Word Problems - International Brotherhood of Electrical Workers Exam IBEW

1. A worker completes a job in $6$ hours. What is the worker's rate in jobs per hour?

   $\frac{1}{6}$ job/hour. Rate is reciprocal of time, so $1$ job divided by $6$ hours.

2. What is the common translation of "of" in an algebraic word statement (as used in percent problems)?

   $\times$. 'Of' translates to multiplication in percent word problems.

3. What is the average speed formula in terms of total distance $D$ and total time $T$?

   $v_{avg}=\frac{D}{T}$. Average speed is total distance divided by total time.

4. A rectangle has perimeter $30$ and width $6$. What is its length?

   $9$. Substitute into $P=2L+2W$ with $P=30$, $W=6$, solve for $L$ by subtracting $12$ and dividing by $2$.

5. What is the percent equation relating part, whole, and percent $p$ (as a decimal)?

   $\text{part}=p\cdot\text{whole}$. The part equals the percent in decimal form multiplied by the whole in percent problems.

6. What number is $30\%$ of $80$?

   $24$. Multiply $80$ by $0.3$ to find $30\%$ of $80$.

7. Two cars start $120$ miles apart and drive toward each other at $50$ mph and $30$ mph. When do they meet?

   $1.5$ hours. Divide distance $120$ by combined speed $80$ mph to find meeting time.

8. Worker A finishes in $4$ hours and worker B in $12$ hours. How long working together?

   $3$ hours. Add rates $\frac{1}{4}$ and $\frac{1}{12}$ to get $\frac{1}{3}$, then take reciprocal for time.

9. The sum of two consecutive integers is $41$. What are the integers?

   $20$ and $21$. Solve $n + (n+1) = 41$ by combining terms, subtracting $1$, and dividing by $2$.

10. What is the simple interest $I$ on $P=200$ at $r=5\%$ for $t=3$ years?

    $30$. Use $I=Prt$ with $P=200$, $r=0.05$, $t=3$ to compute interest.

11. If $5$ more than twice a number is $17$, what is the number?

    $6$. Solve $2x + 5 = 17$ by subtracting $5$ and dividing by $2$.

12. You mix $x$ liters of $20\%$ acid with $10$ liters of $50\%$ acid to get $40\%$. What is $x$?

    $5$. Solve $0.2x + 5 = 0.4(x + 10)$ by expanding, subtracting $0.2x$ and $4$, then dividing by $0.2$.

13. What is the simple interest formula for interest $I$ with principal $P$, rate $r$, time $t$?

    $I=Prt$. Simple interest is principal times annual rate times time in years.

14. What is the mixture equation for total value when mixing amounts $a,b$ at unit values $v_1,v_2$?

    $\text{total value}=av_1+bv_2$. Total value equals sum of each amount times its unit value in mixtures.

15. What is the work-rate equation for two workers with rates $r_1$ and $r_2$ working together for time $t$?

    $\text{work}=(r_1+r_2)t$. Combined work equals sum of rates times time when working together.

16. How long does it take to travel $150$ miles at $50$ miles per hour?

    $3$ hours. Divide distance $150$ by rate $50$ to find time using $t=d/r$.

17. What is the original price if a $20\%$ discount gives a sale price of $48$?

    $60$. Divide sale price $48$ by $0.8$ since $20\%$ discount means $80\%$ of original.

18. What is the perimeter formula for a rectangle with length $L$ and width $W$?

    $P=2L+2W$. Perimeter equals twice length plus twice width for a rectangle.

19. What is the final amount after increasing $120$ by $15\%$?

    $138$. Multiply $120$ by $1.15$ to apply a $15\%$ increase.

20. What percent of $50$ is $15$? Give the percent as a whole number.

    $30\%$. Divide $15$ by $50$ and multiply by $100$ to find the percentage.

21. What is the area formula for a rectangle with length $L$ and width $W$?

    $A=LW$. Area equals length times width for a rectangle.

22. What is the distance-rate-time relationship for constant speed?

    $d=rt$. Distance equals rate multiplied by time at constant speed.

23. What is the common translation of "is" in an algebraic word statement?

    $=$. 'Is' translates to the equals sign in algebraic equations.

24. If $3$ less than one-half a number is $5$, what is the number?

    $16$. Solve $\frac{1}{2}x - 3 = 5$ by adding $3$ and multiplying by $2$.

25. A rectangle has area $48$ and length $12$. What is its width?

    $4$. Substitute into $A=LW$ with $A=48$, $L=12$, solve for $W$ by dividing.

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