Two friends, Becky and Lucia, are growing out their hair. They plan to cut it off at a certain point and donate it to a charity that makes wigs for people with cancer. Becky's hair is already 30 centimeters long and grows at a constant rate of 2 centimeters per month. Lucia's hair is 12 centimeters and growing at a speed of 3 centimeters per month. If the girls get their hair cut on a certain day, they will have exactly the same length to donate. How long will their hair be? How long will that take?

Two friends, Becky and Lucia, are growing out their hair. They plan to cut it off at a certain point and donate it to a charity that makes wigs for people with cancer. Becky's hair is already 30 centimeters long and grows at a constant rate of 2 centimeters per month. Lucia's hair is 12 centimeters and growing at a speed of 3 centimeters per month. If the girls get their hair cut on a certain day, they will have exactly the same length to donate. How long will their hair be? How long will that take?

Name: **Educational Content on Solving a System of Equations****Title: How
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Description: **Educational Content on Solving a System of Equations****Title: How to Use Systems of Equations in Real-World Scenarios**Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.**Scenario:** Two

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Unitary Method

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Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

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**Educational Content on Solving a System of Equations**

**Title: How to Use Systems of Equations in Real-World Scenarios**

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

**Scenario:**
Two friends, Becky and Lucia, are growing out their hair. They plan to cut it off at a certain point and donate it to a charity that makes wigs for people with cancer. Becky’s hair is already 30 centimeters long and grows at a constant rate of 2 centimeters per month. Lucia’s hair is 12 centimeters long and growing at a speed of 3 centimeters per month. If the girls get their hair cut on a certain day, they will have exactly the same length to donate. How long will their hair be? How long will that take?

Their hair will be ___ centimeters in ___ months.

**Instructions:**

1. **Set Up the Equations:**
- Let $ x $ be the number of months it takes for their hair to reach the same length.
- Becky’s hair equation: $ 30 + 2x $
- Lucia’s hair equation: $ 12 + 3x $

2. **Solve the System of Equations:**
- Set the two equations equal to each other:
$ 30 + 2x = 12 + 3x $

3. **Find the Solution:**
- Solve for $ x $ to find the number of months.

4. **Calculate the Length:**
- Substitute $ x $ back into either equation to find the length of the hair at that time.

**Submit your answer:**
Their hair will be ______ centimeters in ______ months.

**Note:** There are no graphs or diagrams included in this problem.

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