A sprout in jessie's garden is 5 1/5cm tall and is growing 1 3/10 cm each week. Write and solve an equation in order to determine how many weeks it will take for the plant to be 13cm tall.

Let's set up an equation to determine how many weeks it will take for the sprout to reach a height of 13 cm.

### Given:
- Initial height of the sprout: \( 5 \frac{1}{5} \) cm
- Growth per week: \( 1 \frac{3}{10} \) cm
- Final desired height: 13 cm

### Convert mixed numbers to improper fractions:

\[
5 \frac{1}{5} = \frac{26}{5} \quad \text{and} \quad 1 \frac{3}{10} = \frac{13}{10}
\]

### Let \( w \) be the number of weeks. The height of the sprout after \( w \) weeks will be:

\[
\text{Height after } w \text{ weeks} = \frac{26}{5} + w \times \frac{13}{10}
\]

### Set this equal to the final desired height:

\[
\frac{26}{5} + w \times \frac{13}{10} = 13
\]

### Solve the equation:

1. Subtract \( \frac{26}{5} \) from both sides:

\[
w \times \frac{13}{10} = 13 - \frac{26}{5}
\]

2. Convert 13 to a fraction with a denominator of 5 to make the subtraction easier:

\[
13 = \frac{65}{5}
\]

So the equation becomes:

\[
w \times \frac{13}{10} = \frac{65}{5} - \frac{26}{5} = \frac{39}{5}
\]

3. Now, solve for \( w \):

\[
w = \frac{\frac{39}{5}}{\frac{13}{10}} = \frac{39}{5} \times \frac{10}{13} = \frac{390}{65} = 6
\]

### Answer:
It will take **6 weeks** for the sprout to reach a height of 13 cm.

Would you like more details or have any other questions?

Here are some related questions:
1. What would be the height after 4 weeks?
2. How tall would the plant be after 10 weeks?
3. If the plant grew 2 cm per week, how many weeks would it take to reach 13 cm?
4. How does changing the initial height affect the number of weeks required?
5. Can you calculate the total growth after a certain number of weeks?

**Tip:** Always convert mixed numbers to improper fractions for easier calculations in algebraic equations.

A sprout in Jessie's garden is 5 1/5 cm tall and is growing 1 3/10 cm each week. Write and solve an equation in order to determine how many weeks it will take for the plant to be 13 cm tall.

Learn how to solve a real-life math problem involving linear equations to find out how many weeks it will take for a sprout to reach 13 cm in height, given its initial height and weekly growth rate. Suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation