Question

. In 2004, three wide receivers, for the Indianapolis Colts caught a total of 37 touchdown passes. Reggie caught 2 more than Brandon. Marvin caught 3 more than Reggie. How many touchdown passes did each receiver catch?

Answer 1

Let be "r" the number of touchdown passes Reggie caught, "b" the number of touchdown passes Brandon caught and "m" of touchdown passes Marvin caught.

With the information give in the problem, you can set up this System of equations:

`\mleft\{\begin{aligned}r+b+m=37 \\ r=b+2 \\ m=r+3\end{aligned}\mright.`

To solve it you can follow these steps:

1. Solve for "b" from the second equation:

`\begin{gathered} r=b+2 \\ r-2=b \\ b=r-2 \end{gathered}`

2. Substitute this fourth equation and the third equation into the first one and solve for "r":

`\begin{gathered} r+b+m=37 \\ r+(r-2)+(r+3)=37 \\ 3r+1=37 \\ r=(37-1)/(3) \\ r=12 \end{gathered}`

3. Knowing "r", you can find "m" and "b" by substituting its value in the corresponding equations:

- For "b":

`\begin{gathered} b=r-2 \\ b=12-2 \\ b=10 \end{gathered}`

- For "m":

`\begin{gathered} m=r+3 \\ m=12+3 \\ m=15 \end{gathered}`

Therefore, Reggie caught 12 touchdown passes, Brandon caught 10 touchdown passes and Marvin caught 15 touchdown passes.