*Contributor: Jamie Hagler. Lesson ID: 13827*

You are having a party! How can you make sure you stay on budget and invite all your friends? With linear equations, of course!

categories

subject

Math

learning style

Visual

personality style

Golden Retriever

Grade Level

High School (9-12)

Lesson Type

Skill Sharpener

Your little brother will turn 10 next month. As your gift to him, you want to throw him a birthday party at his favorite ice cream parlor.

- Do you have enough money in your budget to invite all his friends?

You only have a certain amount in your budget to throw a birthday party for your brother, so you definitely want to make sure that you do not overspend.

- Did you know that there is a way to write an equation to help you figure this out?

Let's give it a try!

First, check out the flyer below with the ice cream parlor's birthday party rates:

If you only have a few kids to invite, it is not too difficult to determine the cost.

- But what if you want to invite a lot of kids?
- Or what if you want to determine how many kids you can invite based on your budget?

Here's how to set up an equation to help you!

Let *T *represent the total cost, and have *k* represent the number of kids.

The $30 setup fee (which is paid just once) plus $7 per kid equals the total cost. The equation will look like this:

- How much would it cost to have 11 kids at the party?

It's 11 kids, so 11 will go in the place of *k*:

30 | + | 7k |
= | T |
|||

30 | + | 7(11) | = | T |
← Substitute 11 for k. |
||

30 | + | 77 | = | T |
← Multiply 7 times 11. | ||

107 | = | T |

So, the total cost would be $107 to include 11 kids at the party.

- What do you do if you know the amount of money you have to spend but don't know the number of kids that it will cover?

Let's say you have $135 to spend.

- How do you set it up?

The total cost would be $135, so 135 will go in the place of *T*.

30 | + | 7k |
= | T |
|||

30 | + | 7k |
= | 135 | ← Substitute 135 for T. |
||

- | 30 | - | 30 | ← Subtract 30 from both sides. | |||

7k |
= | 105 | |||||

7 | 7 | ← Divide both sides by 7. | |||||

k |
= | 15 |

So, you could have 15 kids at the party.

And that's how to solve linear equations! Always look to see where you need to substitute the numbers and then solve!

Now that you have a handle on solving linear equations, let's move on to the *Got It? * section.

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