Solving worded problems

Defining a pronumeral, writing an equation from a worded problem, solving it and answering in words.

Four steps

Example 1●●

The sum of three consecutive whole numbers is $57$. Find them.

Let the numbers be $n$, $n + 1$, $n + 2$.

$3n + 3 = 57$, so $3n = 54$ and $n = 18$.

The numbers are $18$, $19$ and $20$.

Example 2●●

A rectangle is $5$ cm longer than it is wide, and its perimeter is $46$ cm. Find its width.

Let the width be $w$. Then $2w + 2(w + 5) = 46$.

$4w + 10 = 46$, so $w = 9$.

The width is $9$ cm.

Example 3●●●

A plumber charges a $\$60$ call-out fee plus $\$80$ per hour. A bill is $\$300$. How long did the job take?

$60 + 80h = 300$

$80h = 240$, so $h = 3$. The job took $3$ hours.

Flashcards

Consecutive numbers

$n$, $n + 1$, $n + 2$

Consecutive even numbers

$n$, $n + 2$, $n + 4$

Last step

Answer in words with units.

Practice

Three consecutive whole numbers add to $57$. What is the smallest?
A rectangle is $5$ cm longer than it is wide, perimeter $46$ cm. Width in cm?
Call-out $\$60$ plus $\$80$ per hour, bill $\$300$. Hours?
I think of a number, double it and add $7$. The result is $35$. What is the number?
Sam is $3$ times as old as Kim. Their ages add to $48$. How old is Kim?
Two consecutive even numbers add to $46$. What is the smaller one?
Tickets cost $\$15$ each plus a $\$20$ booking fee. A group paid $\$620$. How many tickets?
The angles of a triangle are $x^\circ$, $2x^\circ$ and $30^\circ$. Find $x$.