Math Practice

Algebra Word Problems Practice Problems

Q: How do I choose what x represents?

Let $x$ be the simplest unknown, phrased plainly, and write every other unknown as an expression in that same $x$. Two separate letters would need two equations.

Fifteen hand-built word problems that turn into linear equations, with complete solutions. Each one shows how to choose the variable, translate the sentence into an equation, solve it, and check the answer against the words.

1.
Six more than three times a number is 27. Find the number.
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Let $x$ be the number.
$$ 3x + 6 = 27 \quad\Longrightarrow\quad 3x = 21 \quad\Longrightarrow\quad x = 7 $$
Check: $3(7) + 6 = 27$. ✓ The number is $7$.
2.
The sum of two consecutive integers is 85. Find them.
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Let the smaller be $x$; the next is $x + 1$.
$$ x + (x + 1) = 85 \quad\Longrightarrow\quad 2x + 1 = 85 \quad\Longrightarrow\quad x = 42 $$
The integers are $42$ and $43$.
3.
One number is 7 more than another. Their sum is 51. Find both numbers.
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Let $x$ be the smaller; the larger is $x + 7$.
$$ x + (x + 7) = 51 \quad\Longrightarrow\quad 2x + 7 = 51 \quad\Longrightarrow\quad x = 22 $$
The numbers are $22$ and $29$.
4.
A 90-cm wire is cut into two pieces so that one piece is 4 times the length of the other. Find both lengths.
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Let $x$ be the shorter piece; the longer is $4x$.
$$ x + 4x = 90 \quad\Longrightarrow\quad 5x = 90 \quad\Longrightarrow\quad x = 18 $$
The pieces are $18$ cm and $72$ cm.
5.
Three times a number, decreased by 5, is the same as the number increased by 11. Find the number.
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$$ 3x - 5 = x + 11 \quad\Longrightarrow\quad 2x = 16 \quad\Longrightarrow\quad x = 8 $$
The number is $8$.
6.
Ten less than four times a number equals twice the number plus 8. Find the number.
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$$ 4x - 10 = 2x + 8 \quad\Longrightarrow\quad 2x = 18 \quad\Longrightarrow\quad x = 9 $$
The number is $9$.
7.
The sum of three consecutive even integers is 138. Find them.
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$$ x + (x + 2) + (x + 4) = 138 \quad\Longrightarrow\quad 3x + 6 = 138 \quad\Longrightarrow\quad x = 44 $$
The integers are $44$, $46$, and $48$.
8.
The sum of three consecutive odd integers is 165. Find them.
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$$ x + (x + 2) + (x + 4) = 165 \quad\Longrightarrow\quad 3x + 6 = 165 \quad\Longrightarrow\quad x = 53 $$
The integers are $53$, $55$, and $57$.
9.
The larger of two numbers is 3 less than 4 times the smaller. Their sum is 42. Find both.
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Let $x$ be the smaller; the larger is $4x - 3$.
$$ x + (4x - 3) = 42 \quad\Longrightarrow\quad 5x - 3 = 42 \quad\Longrightarrow\quad x = 9 $$
The numbers are $9$ and $33$.
10.
The sum of four consecutive integers is 130. Find them.
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$$ x + (x+1) + (x+2) + (x+3) = 130 \quad\Longrightarrow\quad 4x + 6 = 130 \quad\Longrightarrow\quad x = 31 $$
The integers are $31$, $32$, $33$, $34$.
11.
A jar of dimes and quarters has 3 times as many dimes as quarters, and 40 coins total. How many of each?
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Let $x$ be the quarters; dimes are $3x$.
$$ x + 3x = 40 \quad\Longrightarrow\quad 4x = 40 \quad\Longrightarrow\quad x = 10 $$
$10$ quarters and $30$ dimes.
12.
A box holds 54 pens, all blue or black. There are 6 more black pens than twice the number of blue pens. How many of each?
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Let $x$ be the blue pens; black is $2x + 6$.
$$ x + (2x + 6) = 54 \quad\Longrightarrow\quad 3x + 6 = 54 \quad\Longrightarrow\quad x = 16 $$
There are $16$ blue and $38$ black. Check: $16 + 38 = 54$. ✓
13.
A mother is 4 times as old as her daughter. In 16 years she will be twice as old as the daughter is then. Find their current ages.
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Let $x$ be the daughter's age now; the mother is $4x$.
$$ 4x + 16 = 2(x + 16) \quad\Longrightarrow\quad 4x + 16 = 2x + 32 \quad\Longrightarrow\quad 2x = 16 \quad\Longrightarrow\quad x = 8 $$
The daughter is $8$; the mother is $32$. In 16 years: $24$ and $48$, and $48 = 2 \times 24$. ✓
14.
Kim is 5 years older than Lee. Three years ago, Kim was twice as old as Lee was then. Find their current ages.
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Let $x$ be Lee's age now; Kim is $x + 5$. Three years ago: Lee was $x - 3$, Kim was $x + 2$.
$$ x + 2 = 2(x - 3) \quad\Longrightarrow\quad x + 2 = 2x - 6 \quad\Longrightarrow\quad x = 8 $$
Lee is $8$, Kim is $13$. Check three years ago: $5$ and $10$. ✓
15.
Twice the sum of a number and 4 is 6 more than the number. Find the number.
Show full solution
$$ 2(x + 4) = x + 6 \quad\Longrightarrow\quad 2x + 8 = x + 6 \quad\Longrightarrow\quad x = -2 $$
The number is $-2$. Check: $2(-2 + 4) = 4$ and $-2 + 6 = 4$. ✓

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Algebra Word Problems Practice Problems

The Word Problems lesson gives a five-step method and a full translation table; this set is 15 problems to practice it on, each with a complete worked solution.

How to use this set

These problems are hand-written, not auto-generated. Work each one on paper first — choose the variable, write the equation, solve, and check — then open the solution to compare. The value is in the setup, so write out every step.

Common mistakes to watch for

Using a different letter for every unknown. One variable with expressions needs only one equation.

Reversing a subtraction. “7 less than ” is , not .

Forgetting parentheses after “the sum of… , doubled.” , not .

Stopping at . If the question asks for the largest integer or the number of dimes, translate back.

Where to go next

For the specialized types, see the Distance, Rate, and Time Practice Problems, Work Problems Practice Problems, and Mixture Problems Practice Problems. For the full method, see the Word Problems lesson.

Frequently Asked Questions

How is this practice set organized?+

It is a hand-written set of 15 problems rather than auto-generated ones, because word problems don't translate into a single auto-checkable number. Each problem has a full worked solution you can open after attempting it.

What is the hardest part of a word problem?+

The translation — reading the sentence and writing the right equation. Once the equation is written, it is solved with ordinary linear-equation techniques.

How do I choose what x represents?+

Let be the simplest unknown, phrased plainly, and write every other unknown as an expression in that same . Two separate letters would need two equations.

Why check the answer against the words and not just the equation?+

A value can solve the equation but be impossible in context — a negative age, a fractional person. That means the equation was set up wrong, so you fix the translation, not the arithmetic.

How do age problems work?+

Everyone ages at the same rate. Set up 'now' ages first, then shift both people by the same number of years for a past or future condition.

Are the motion, work, and mixture word problems here?+

No — those have their own dedicated practice sets. This set covers number, age, consecutive-integer, and part-of-a-whole problems.

📝Algebra Word Problems Practice Problems

Algebra Word Problems Practice Problems

How to use this set

Common mistakes to watch for

Where to go next

Frequently Asked Questions

More practice problems

Algebra Word Problems Practice Problems