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Art and chris had a two-month competition to see who could walk more dogs. in the first month, art walked 3/5 as many dogs as chris. during the second month, Art increased the number of dogs he walked by 5 and Chris lost 4 customers. in the second month, art walked 25 dogs less than chris. how many dogs did each boy walk each month?

User Frmsaul
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1 Answer

6 votes

Ok, so

We know that Art and Chris had a two month competition to see who could walk more dogs.

Let "x" be the number of dogs that Art walked and let "y" be the number of dogs that Chris walked.

In the first month, we could write:


x=(3)/(5)y

In the second month, we have that:


x=y-25

And, in the first month,


x-5=(3)/(5)(y+4)

We could solve the system:


\begin{gathered} x-5=(3)/(5)(y+4) \\ x=y-25 \end{gathered}

If we re-write:


\begin{gathered} \begin{cases}x-5=(3)/(5)y+(12)/(5) \\ x=y-25\end{cases} \\ \\ \begin{cases}x=(3)/(5)y-(12)/(5)+5 \\ x=y-25\end{cases} \end{gathered}

By equal values method, we could write:


\begin{gathered} (3)/(5)y+(37)/(5)=y-25 \\ (3y+37)/(5)=y-25 \\ 3y+37=5(y-25) \\ 3y=5y-125-37 \\ -2y=-162 \\ y=81 \end{gathered}

The total number of dogs that Chris walked in the second month, was 81.

Now, replacing:


\begin{gathered} x=y-25 \\ x=81-25 \\ x=56 \end{gathered}

The total number of dogs that Chris walked in the second month, was 56.

During the second month, art increased the number of dogs he walked by 5 and chris lost 4 customers, so, in the first month, Art had 5 dogs less, and Chris had 4 dogs more. Then, in the first month:


\begin{gathered} x=51 \\ y=85 \end{gathered}

Which clearly is:


\begin{gathered} x=(3)/(5)y \\ 51=(3)/(5)(85) \end{gathered}

Therefore, in the second month, Art walked 56 dogs and Chris walked 81 dogs.

In the first month, Art walked 51 dogs and Chris walked 85 dogs.

User Cory Foy
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