Word Problems - GED Math

1. A brother is 4 years older than twice his sister's age $s$. Write an expression for his age.

   $2s + 4$. Double her age first, then add $4$.

2. Which inequality symbol does the phrase "at least" translate to?

   $\ge$ (greater than or equal to). "At least 18" means $x \ge 18$.

3. A van can carry at most $1{,}200$ pounds. Each box weighs $40$ pounds. Write an inequality for the number of boxes $b$.

   $40b \le 1{,}200$. "At most" means less than or equal to.

4. A rectangle's length is $3$ more than its width $w$. Write an expression for its perimeter.

   $4w + 6$. $P = 2w + 2(w + 3)$.

5. If $n$ is the smallest of three consecutive integers, what expression gives their sum?

   $3n + 3$. The integers are $n$, $n + 1$ and $n + 2$.

6. What operation does the word "per" usually signal in a word problem?

   Division, giving a rate. For example, miles per hour is miles divided by hours.

7. In a percent word problem, what operation does the word "of" usually signal?

   Multiplication. For example, $30\%$ of $n$ is $0.3n$.

8. Write an equation for "a number $n$ increased by 8 is 20."

   $n + 8 = 20$. "Increased by" means add, and "is" means equals.

9. A phone plan costs 30 dollars a month plus 0.10 dollars per text. Write the monthly cost $C$ for $t$ texts.

   $C = 30 + 0.10t$. The fixed fee is the constant; the per-text charge multiplies $t$.

10. A car travels at $55$ miles per hour for $t$ hours. Write an expression for the distance.

    $55t$ miles. Distance equals rate times time: $d = rt$.

11. Tickets cost 12 dollars each plus a 5 dollar fee per order. One order totals 77 dollars. Write an equation for the number of tickets $t$.

    $12t + 5 = 77$. The per-ticket cost multiplies $t$; the fee is added once. (It gives $t = 6$.)

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