Multi-step word problems (averages and percentages)

Averages and percentages occur all the time in real life. Shops offer a percentage off during sales and you'll often hear the average price of petrol advertised on the news. These problems are often word problems but as you know, we can write worded problems mathematically to help us solve them. 

Sometimes we can solve these kinds of problems as number equations but sometimes it's easier to solve them with algebraic ones instead.

As we saw when we looked at worded arithmetic problems, we need to convert the worded problem into an equation, then solve it as a multi-step equation. 

Let's look through some examples of word problems that involve averages and percentages now.

 

Examples

Question 1

David wants to know, on average, how many pets his friends have. 

He has asked a group of his friends, and his results are below:

$6,1,1,4$6,1,1,4

What is the average number of pets among his friends?

Think: To find the average or mean, we need to divide the sum of the scores by the number of scores.

Do:

$\text{Average }$Average	$=$=	$\frac{6+1+1+4}{4}$6+1+1+44​
	$=$=	$\frac{12}{4}$124​
	$=$=	$3$3 pets

 

Question 2

Han wants to try out as a batsman for a cricket team. In his last three matches, he scored $61$61, $75$75 and $66$66 runs. In his last match before trying out, he wants to lift his average to $70$70. If $x$x is the number of runs he needs to score to achieve this, find $x$x.

 

Question 3

In a fire sale, a store sold goods at $41%$41% below cost in order to reduce inventory to zero. If $\$13900$$13900 was generated from the sale, calculate the cost of goods sold (to the nearest cent.