Grade 6 Math · Topic 47

Writing Equations from Word Problems

An equation is a statement that two expressions are equal. To set one up from a word problem, choose a variable for the unknown, translate the words into expressions, and use = for words like is, equals, totals, results in.

Lesson alignment: 6.EE.B.7 · 6.EE.C.9 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Connect two changing quantities

A game costs $2 to enter plus $3 for each game played. Change one quantity and follow it through the table, graph, and equation.

Think first: If one more game is played, how should the total cost change? How will that appear in the table and graph?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Connect a context, table, graph, and equation

The independent variable is the input you choose. Here, let x be the number of games played. The dependent variable is the output that changes in response: let y be the total cost in dollars.

A game room charges a $2 entry fee plus $3 for each game. The total cost is y = 3x + 2.

Each table row is one ordered pair (x, y)
Games, xTotal cost, yGraph point
0$2(0, 2)
1$5(1, 5)
2$8(2, 8)
3$11(3, 11)

Every row follows the same rule: multiply the number of games by 3, then add the $2 entry fee. A row's pair becomes a point on the graph. When x increases by 1, y increases by $3.

Try the same thinking in a new situation

A skating rink charges $4 to enter plus $2 for each skate rental. Let r be the number of rentals and C the total cost. Write an equation, complete a small table for 0, 1, 2, and 3 rentals, then name the point for 3 rentals.

Show one way to reason it out

The entry fee is the starting amount, $4. Each rental adds $2, so C = 2r + 4. For r = 0, 1, 2, and 3, the costs are $4, $6, $8, and $10. The point for 3 rentals is (3, 10).

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

“Five more than a number is 12.” Write the equation.

Let x be the number. “Five more than x” is x + 5. “Is 12” means = 12. So x + 5 = 12.

Answer: x + 5 = 12

Worked example 2

“Three times a number, decreased by 4, equals 20.” Write the equation.

Let n be the number. 3n - 4 = 20.

Answer: 3n - 4 = 20

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. The sum of x and 7 is 15.
    Check

    x+7=15

  2. Twice x equals 18.
    Check

    2x=18

  3. x less than 20 equals 8.
    Check

    20-x=8

  4. 5 more than x is 11.
    Check

    x+5=11

  5. Half of x is 9.
    Check

    (x)/2=9

  6. Triple x plus 2 equals 17.
    Check

    3x+2=17

  7. x divided by 4 is 6.
    Check

    (x)/4=6

  8. Four less than twice x is 14.
    Check

    2x-4=14

Try this situation 1

A box holds some balls. Adding 7 more makes 20 in total. Write an equation.

Show a worked solution

Answer: x + 7 = 20.

Let x = original count of balls; “adding 7 makes 20” becomes x + 7 = 20.

Try this situation 2

Marco bought a backpack for $15 and some books costing $8 each. He spent $47 in all. Write an equation for the number of books b.

Show a worked solution

Answer: 15 + 8b = 47.

$15 fixed plus $8 each for b books equals total $47.

Fresh questions · saved on this device

Practice this skill

31 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A game room charges 2 dollars to enter plus 3 dollars for each game. If x is the number of games and y is the total cost, which variable is independent?

2. A skating rink charges 4 dollars to enter and 2 dollars per rental. Which equation gives total cost C for r rentals?

3. A table has the row x = 2 and y = 10. What does the graph point (2, 10) represent?

4. A cost table starts at 6 dollars when h = 0 and increases 3 dollars for each hour. Which equation matches the table?

5. The relationship is y = 4x + 1. What ordered pair belongs in the table and graph when x = 3?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Expressions, Equations & Inequalities quiz ↗Try a full practice test ↗