College

We appreciate your visit to Two teams participate in a charity run Each team includes runners and supporters The total registration fee for 2 runners and 1 supporter in Team. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Two teams participate in a charity run. Each team includes runners and supporters. The total registration fee for 2 runners and 1 supporter in Team A is [tex]$60[/tex]. The total registration fee for 6 runners and 5 supporters in Team B is [tex]$220[/tex].

Write a system of equations to find out how much each ticket costs.

Answer :

To find the registration fees for runners and supporters in the charity run, we need to set up a system of equations based on the given problem and then solve it. Let’s break it down step-by-step:

1. Define the Variables:
- Let [tex]\( r \)[/tex] be the registration fee for a runner.
- Let [tex]\( s \)[/tex] be the registration fee for a supporter.

2. Set Up the Equations:
- From Team A, we know that the total fee for 2 runners and 1 supporter is [tex]$60. So, the equation is:
\[
2r + s = 60
\]
- From Team B, we know that the total fee for 6 runners and 5 supporters is $[/tex]220. So, the equation is:
[tex]\[
6r + 5s = 220
\][/tex]

3. Solve the System of Equations:
- We have the system of equations:
[tex]\[
\begin{align*}
2r + s &= 60 \\
6r + 5s &= 220
\end{align*}
\][/tex]

4. Elimination Method:
- First, let's eliminate [tex]\( s \)[/tex] by making the coefficients of [tex]\( s \)[/tex] the same in both equations. We can achieve this by multiplying the first equation by 5:
[tex]\[
\begin{align*}
10r + 5s &= 300 \quad \text{(Equation 1 multiplied by 5)} \\
6r + 5s &= 220 \quad \text{(Equation 2 unchanged)}
\end{align*}
\][/tex]
- Subtract the second equation from the new first equation:
[tex]\[
(10r + 5s) - (6r + 5s) = 300 - 220
\][/tex]
[tex]\[
4r = 80
\][/tex]
- Solve for [tex]\( r \)[/tex]:
[tex]\[
r = \frac{80}{4} = 20
\][/tex]

5. Substitute Back to Find [tex]\( s \)[/tex]:
- Use the value of [tex]\( r \)[/tex] in the first equation [tex]\( 2r + s = 60 \)[/tex]:
[tex]\[
2(20) + s = 60
\][/tex]
[tex]\[
40 + s = 60
\][/tex]
[tex]\[
s = 60 - 40 = 20
\][/tex]

6. Solution:
- The registration fee for a runner is [tex]$20.
- The registration fee for a supporter is $[/tex]20.

Both the runner's and supporter's registration fees are $20 each based on the set of information given.

Thanks for taking the time to read Two teams participate in a charity run Each team includes runners and supporters The total registration fee for 2 runners and 1 supporter in Team. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada