# Means in Word Problems

Finding a mean or an average in a word problem is often quite simple.

**To find a mean, you add up the data points and divide by the number of datapoints.** Because people often find means in real life, it's easy to do word problems of this type.

**The simplest type of mean or average word problem simply requires you to read a word problem to find the data, and then find the mean (or average).**

*Example:* You and your siblings went strawberry picking. You picked 20 strawberries. Your big brother picked 28 strawberries and your baby sister picked 4. What is the average number of strawberries that the children in your family picked?

Start with the formula (this may seem silly, but it's gives you a good starting point for any word problem that uses means):

$\dfrac{\text{Sum of datapoints}}{\text{Number of datapoints}}=\text{Mean of data}$

Plug in your data:

$$\eqalign{\dfrac{20+28+4}{3}&=\text{Mean of data}\\\dfrac{52}{3}&=17.333}$$

You and your siblings picked an average of $17.33$ strawberries each.

**However, word problems sometimes don't just give you the datapoints. In a word problem, you can be given the average and asked to find a datapoint (or the sum of the datapoints).**

To do any of these problems, you want to remember the formula for finding a mean:

$\dfrac{\text{Sum of datapoints}}{\text{Number of datapoints}}=\text{Mean of data}$

Then, you read the word problem and plug the information that the problem gives you into the formula.

*Example*: You have taken four math tests and received the following scores: 8, 9, 7, 10, 7. If, after you take a 6th test, the mean of your scores is 8, what was your 6th test score?

Start with the formula:

$\dfrac{\text{Sum of scores}}{\text{Number of scores}}=\text{Mean of scores}$

What do you know?

Sum of scores: $8+9+7+10+7+x$ (x is the 6th score that you don't know)

Number of scores: $6$

Mean of scores: $8$

Plug what you know into the equation:

$$\eqalign{\dfrac{\text{Sum of scores}}{\text{Number of scores}}&=\text{Mean of scores}\\\\\dfrac{8+9+7+10+7+x}{6}&=8}$$

Then solve the equation:

$$\eqalign{\dfrac{8+9+7+10+7+x}{6}&=&&8\\\dfrac{41+x}{6}&=&&8\\6\times(\dfrac{41+x}{6})&=&&8\times 6\\41+x&=&&48\\-41\text{ }&\text{}&&-41\\x&=&&7}$$

Your final score was $7$.

Overall, whenever you face a word problem that uses means or averages, start with the formula, plug in what you know, and do the math. You'll solve the problem!

#### Practice Problems:

## Means in Word Problems

- Kelly makes an average of five pies an hour for six hours on Monday and for eight hours on Tuesday. What is the average number of pies she makes per day?
- Val helps an average of ten customers an hour for four hours on Thursday and for six hours on Friday. What is the average number of customers she sees per day?
- Mark washes an average of five dogs an hour for seven hours on Saturday and for three hours on Sunday. What is the average number of dogs he washes per day?
- Bonnie and Clyde collect action figures. If Bonnie has 8 action figures and Clyde has four times as many as Bonnie, what is the average number of action figures in their collections?
- Ernie and Bert collect stamps. If Ernie has 15 stamps and Bert has twice as many stamps as Ernie does, what is the averge number of stamps that the boys have?
- Donna and Joyce collect postcards. If Donna has 7 postcards and Joyce has three times as many postcards as Donna does, what is the average number of postcards in the girls' collections?
- Joseph and Jenny collect erasers. If Joseph has 14 erasers and Jenny has four times as many erasers as Joseph has, what is the average number of erasers in the friends' collections?
- Allison and Andrew are each growing a garden. If Allison has grown 12 sunflowers and Andrew has grown half as many, what is the average number of sunflowers in their gardens?
- John scored 90, 75, and 87 on history tests. What is his average score?
- As he played video games one day, Jesse scored an average of 15 points per game for 5 games. How many points did he score in all five games combined?
- In a restaurant, Luigi, the chef, made an average of 200 sandwiches per day for three days. How many sandwiches did he make over the course of the three days?
- Jason, an all-star basketball player, successfully made an average of 12 shots per minute for 7 minutes. How many shots did he make over the seven minute period?

#### Answer Key: