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9E

Using equations to solve problems

Turning word problems into equations, solving them, and answering the question in words.

Four steps

Example 1●●

I think of a number, triple it and add $8$. The result is $41$. What is the number?

Let the number be $n$. Then $3n + 8 = 41$.
$3n = 33$, so $n = 11$.
The number is $11$. Check: $33 + 8 = 41$.
Example 2●●

A rectangle is $5$ cm longer than it is wide and its perimeter is $50$ cm. Find its width.

Let the width be $w$ cm. Length $= w + 5$.
$2w + 2(w + 5) = 50$, so $4w + 10 = 50$.
$4w = 40$, so $w = 10$. The width is $10$ cm.
Flashcards
Step 1 of a word problem
Let a pronumeral stand for the unknown.
Consecutive numbers
$n$, $n + 1$, $n + 2$
Last step
Answer the question in words.
Practice

  1. Triple a number and add $8$ to get $41$. Find the number.

  2. A rectangle is $5$ cm longer than wide with perimeter $50$ cm. Find the width.

  3. Three consecutive numbers add to $48$. Find the smallest.

  4. A taxi charges $\$4$ plus $\$2.50$ per km. A trip cost $\$21.50$. How many km?

  5. Jo is $3$ times as old as her son. Their ages add to $48$. How old is the son?

  6. Half a number minus $5$ is $8$. Find the number.

  7. "Five more than twice a number is $17$" is:

  8. Two angles on a straight line are $x^\circ$ and $(2x + 30)^\circ$. Find $x$.

More questions

New numbers every time. Keep going until you get five in a row.

Formula sheet