# 1.18: Problem Solving Plan, Mental Math

**At Grade**Created by: CK-12

**Practice**Applications Using Linear Models

Remember the elephants in the last Concept? Well, you could have used mental math to solve that problem instead of guess, check and revise. Here it is again.

There are two elephants at the city zoo, and they are also two different kinds of elephants. One is an African Elephant and the other is an Indian Elephant. An African elephant is larger than an Indian elephant. One of the fun jobs that city zookeepers get to do is to weigh in the elephants. It is always interesting to see how much each elephant weighs. Tara Jonsen gets the fun job of weighing Jojo, a male African Elephant and Junas, an Indian Elephant. She wonders if just this once Junas will weigh more than Jojo. Jojo weighs 4,000 pounds more than Junas. Their combined weight is 26,000 pounds. Tara leads them both back to their habitats. When she returns to the log book, she realizes that she forgot to write down each specific weight. She remembers two things. That Jojo weighs 4,000 pounds more than Junas. That their combined weight was 26,000 pounds. Given this information, can Tara figure out what each elephant weighed?

**Use this Concept to learn how to use mental math as a problem solving strategy.**

### Guidance

In our last Concept, we worked on reading and understanding a given problem situation. We used this first step of the four-part problem-solving plan as we worked with Tyler and his orangutan adoption problem.

Now we are going to apply this first step to the elephant problem.

Let’s look at the problem once again so that we can determine **the given information** and identify **what information we are looking for.**

**Here is the problem.**

There are two elephants at the city zoo, and they are also two different kinds of elephants. There is an African Elephant and an Indian Elephant. An African elephant is larger than an Indian elephant. One of the fun jobs that city zookeepers get to do is to weigh in the elephants. It is always interesting to see how much each elephant weighs. Tara Jonsen gets the fun job of weighing Jojo, a male African Elephant and Junas, an Indian Elephant. She wonders if just this once Junas will weigh more than Jojo. Jojo weighs 4,000 pounds more than Junas. Their combined weight is 26,000 pounds. Tara leads them both back to their habitats. When she returns to the log book, she realizes that she forgot to write down each specific weight. She remembers two things. That Jojo weighs 4,000 pounds more than Junas. That their combined weight was 26,000 pounds. Given this information, can Tara figure out what each elephant weighed?

**Let’s underline all of the important information.**

**Our given information is:**

**Jojo weighs 4,000 pounds more than Junas.**

**Their combined weight is 26,000 pounds.**

**To understand this problem, we need to figure out two unknowns.** **We need to figure out what Junas weighed and what Jojo weighed.** **There is a relationship between the two weights.**

We can use mental math to solve this problem. If we take the total amount of weight, 26,000 pounds, and subtract 4,000 since that is the difference between the two elephants, we get a new answer.

22,000 pounds

We can next divide it in half for the two elephants.

\begin{align*}22,000 \div 2 = 11,000\end{align*}

That is the weight if the elephants were equal. But one weighs more than the other so we can add 4,000 to 11,000.

Jojo weighs 15,000 pounds

Junas weighs 11,000 pounds

Let's use mental math to solve a few examples.

#### Example A

Travis lives in Florida and loves going to pick strawberries during strawberry season. He can fit 25 strawberries in one box. If he is given a barrel of 500 strawberries, how many boxes will it take for Travis to sort the strawberries?

**Solution: 20 boxes**

#### Example B

If he fills 40 boxes during his shift at work, how many strawberries did he start with?

**Solution: 1000**

#### Example C

If Travis works two shifts, at this rate, how many boxes will he fill?

**Solution: 80 boxes**

Now you know that you can use mental math to help Tara solve the elephant dilemma. Here is the original problem once again.

There are two elephants at the city zoo, and they are also two different kinds of elephants. One is an African Elephant and the other is an Indian Elephant. An African elephant is larger than an Indian elephant. One of the fun jobs that city zookeepers get to do is to weigh in the elephants. It is always interesting to see how much each elephant weighs. Tara Jonsen gets the fun job of weighing Jojo, a male African Elephant and Junas, an Indian Elephant. She wonders if just this once Junas will weigh more than Jojo. Jojo weighs 4,000 pounds more than Junas. Their combined weight is 26,000 pounds. Tara leads them both back to their habitats. When she returns to the log book, she realizes that she forgot to write down each specific weight. She remembers two things. That Jojo weighs 4,000 pounds more than Junas. That their combined weight was 26,000 pounds. Given this information, can Tara figure out what each elephant weighed?

Now let's use mental math to figure out the solution to Tara's problem.

\begin{align*}(x + 4000) + y = 26,000\end{align*}

Remember that one value is 4,000 more than the other value.

We can use mental math to figure this out.

Think about if 10,000 would work.

\begin{align*}(10,000 + 4,000) + 10,000 = 24,000\end{align*}

This would have one elephant weighing 14,000 and one weighing 10,000. Our weights aren't enough.

We can use mental math to figure out how to add 2,000 more pounds.

\begin{align*}(11,000 + 4,000) + 11,000 = 26,000\end{align*}

Jojo weighs 15,000 pounds and Junas weighs 11,000 pounds.

**This is our answer.**

### Vocabulary

Here are the vocabulary words that are found in this Concept.

- Product
- the answer to a multiplication problem

- Quotient
- the answer to a division problem

- Word Problem
- A problem that uses verbal language to explain a mathematical situation.

- Sum
- the answer in an addition problem

- Difference
- the answer in a subtraction problem

### Guided Practice

Here is one for you to try on your own. Look at the examples in the Guidance part of the Concept.

How many strawberries did Travis sort over both shifts?

**Answer**

Travis sorted 1000 strawberries in one shift at work. If he worked two shifts, at the same rate, it means that he sorted 2000 strawberries during the two shifts.

### Video Review

Here is a video for review.

Khan Academy: Word Problem Solving Strategies

### Practice

Directions: Use mental math to solve each of the following problems.

1. Josie helps tag the strawberries. She tags them at \begin{align*}\$2.00\end{align*} per pint. If she sells 100 pints, how much money has she made?

2. If Josie sells $400.00 worth of strawberries, how many pints has she sold?

3. Josie also enjoys making strawberry milkshakes. If it takes 5 strawberries to make one milkshake, how many can she make with 20 strawberries?

4. If Josie makes 35 strawberry milkshakes in one day, how many strawberries does she need to accomplish this task?

5. If there are 25 strawberries in a pint, how many pints does Josie use to make her 35 milkshakes?

6. Carl loves to collect old vinyl records. He has a whole collection that he received from his Dad. If he has five different categories of records with twenty records in each category, how many records does Carl have altogether?

7. Julie is a friend of Carl’s. She brought over her collection of records. Julie has 254 records. If she and Carl were to combine their collections, how many would they have altogether?

8. When Carl and his Mom went to a yard sale, Carl got a box of vinyl records for $25.00. He brought them home and looked in the box. Out of 30 records, five of them were broken or scratched. If he puts these new records with his collection, how many does he now have?

9. Carl’s sister borrowed ten records to show her friend. How many are left in Carl’s collection?

10. Mario is an outstanding skateboarder. He recently purchased a new skateboard. He wants to sell his old one. A friend wishes to buy it for \begin{align*}\$45\end{align*}. If he gives Mario three twenty dollar bills, how much change should Mario give his friend?

11. If Mario buys a new skateboard for double the price that he sold his old one, how much did he pay for the new skateboard?

12. If Mario has \begin{align*}\$100.00\end{align*} and he buys the skateboard for double the price that he sold his old one, does he have enough money to make the purchase?

13. Did he receive any change back at the skateboard shop? How much?

14. Karen collects fairy figurines. She was given 3 for her birthday, 2 for Christmas, 4 from her grandmother and 3 she bought on her own. How many fairy figurines does she have in all?

15. Karen’s little sister loves one of the figurines. Karen has decided to give her the little fairy as a gift. After she does this, how many figurines will Karen have left?

16. At a yard sale, Karen bought 5 fairies for \begin{align*}\$20.00\end{align*}. How much did she pay per fairy?

17. How many fairies does Karen have now?

18. Karen’s friend Emily also collects fairies. If Emily has twice as many fairies as Karen, how many does she have?

19. Jamie runs track at school. He is one of the fastest runners on the team and runs one mile in about 5 minutes. How long will it take Jamie to run 10 miles?

20. If Jamie runs a 3 mile race, about how how much time will it take to run the 3 miles at his one mile pace?

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Difference

The result of a subtraction operation is called a difference.Product

The product is the result after two amounts have been multiplied.Quotient

The quotient is the result after two amounts have been divided.Sum

The sum is the result after two or more amounts have been added together.Word Problem

A word problem is a problem that uses verbal language to explain a mathematical situation.### Image Attributions

Here you'll learn how to solve problems by using mental math.