Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two political activists, Gavin and Isabelle, have a friendly bet to see who can get the most signatures on a petition. So far, Gavin has collected 197 signatures and Isabelle has collected 71 signatures. Gavin is averaging 1 new signature per minute, while Isabelle is managing to collect an average of 4 signatures per minute. Assuming this trend continues, they will have a tie before long. How many signatures will each one have at that point? How long will that take?

Answer 1

Step 1

Given;

`\begin{gathered} \text{Gavin has collected 197 signatures on the bet of the petition} \\ \text{Isabelle has collected 71 signatures on the bet of the petition} \\ \text{Gavin gets 1 signature per minute} \\ \text{Isabelle gets 4 signatures per minute} \end{gathered}`

Required; Find how many signatures each will have if the trend continues and they have a tie.

Step 2

Find the system of equations where x represents the number of minutes

`\begin{gathered} \text{For Gavin(g) number of signatures is given by; g=197 + x} \\ \text{For Isabelle(i) number of signatures is given by; i= 71+4x} \end{gathered}`

Step 3

For there to be a tie, we will equate the number of signatures of Gavi To that of Isabelle

`197+x=71+4x`

Step 4

Find how many signatures each of them will have

`\begin{gathered} 197+1(x)=71+4x \\ 197-71=4x-x \\ 126=3x \\ (3x)/(3)=(126)/(3) \\ x=42 \end{gathered}`

Therefore, Gavin will have the number of signatures below;

`\begin{gathered} g=\text{ 197+42} \\ g=239\text{ signatures} \end{gathered}`

Therefore, Isabelle will have the number of signatures below;

`\begin{gathered} i=71+4(42) \\ i=71+168 \\ i=239\text{ signatures} \end{gathered}`

Hence, both Gavin and Isabelle will have 239 signatures each after 42 minutes