Before you read

Answer first — see what you already know.

A gym membership costs $$25$ per month plus a one-time registration fee of $$50$ . If a member has paid a total of $$275$ , how many months has the member been a part of the gym?

A
$7$
B
$9$
C
$10$
D
$11$

Check your answer

Answer:

Before you read

Answer first — see what you already know.

The sum of two consecutive even integers is 54. What is the larger integer?

A
$26$
B
$27$
C
$28$
D
$30$

Check your answer

Answer:

Theory

Translating Words into Math

The hardest part of word problems is turning English into algebra. Here's a translation guide:

English	Math
is, was, will be, equals	$=$
more than, increased by, added to	$+$
less than, decreased by, subtracted from	$-$
times, of, product of	$\times$
divided by, per, ratio of	$\div$
a number, an unknown quantity	$x$
twice a number	$2x$
5 more than a number	$x + 5$
3 less than a number	$x - 3$

Important: "less than" reverses the order! "5 less than $x$ " means $x - 5$ , NOT $5 - x$ .

Organizing word problem data in a table

Theory

The 4-Step Method

For every word problem:
1. Define your variable: "Let $x$ = ..."
2. Translate the problem into an equation
3. Solve the equation
4. Check that your answer makes sense in context (is it reasonable?)

Example 1

A plumber charges $45 for a house call plus $30 per hour of work. If the total bill was $165, how many hours did the plumber work?

Define: Let $h$ = number of hours worked

Translate: $45 + 30h = 165$

Solve: $30h = 120$ $\to$ $h = 4$

Check: $45 + 30(4) = 45 + 120 = 165$ ✓ and 4 hours is reasonable.

The plumber worked

4

hours.

Example 2

The sum of three consecutive integers is 72. What is the smallest integer?

Define: Let $n$ = the smallest integer. Then the three integers are $n$ , $n + 1$ , $n + 2$ .

Translate: $n + (n + 1) + (n + 2) = 72$

Solve: $3n + 3 = 72$ $\to$ $3n = 69$ $\to$ $n = 23$

Check: $23 + 24 + 25 = 72$ ✓

The smallest integer is

23

Example 3

Maria has $15 more than twice what John has. Together they have $75. How much does John have?

Define: Let $j$ = John's amount. Then Maria has $2j + 15$ .

Translate: $j + (2j + 15) = 75$

Solve: $3j + 15 = 75$ $\to$ $3j = 60$ $\to$ $j = 20$

Check: John = $20, Maria = $55 (since $2(20) + 15 = 55$ ). Total = $75 ✓

John has

\$20

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