Question

In the first three football games of the seasons, Carlos gained 3 times as many yards as Alden. Travis gained 10 years more than Carlos. Altogether the three players gained a total of 430 yards. How many did Carlos gain?

Answer 1

Carlos made 180yds

Explanation:

Let `a` be the number of yards gained by Alden, `c` for Carlos and `t` for Travis.

`c = 3a` , `t = c + 10` and `a + c + t = 430`

`a + 3a + 3a + 10 = 430`

`therefore 7a = 420`

`a = 60`

`c = 3a = 180`

Answer 2

See a solution process below:

Explanation:

First, let's name:

The number of yards Carlos gained: `c`

The number of yards Alden gained: `a`

The number of yards Travis gained: `t`

From the problem we know:

`c = 3a`

and

`t = c + 10`

and

`c + a + t = 430`

We can solve the first equation in terms of `a` as follows:

`c = 3a`

`c/color(red)(3) = (3a)/color(red)(3)`

`c/3 = (color(red)(cancel(color(black)(3)))a)/cancel(color(red)(3))`

`c/3 = a`

`a = c/3`

We can now substitute for `a` and `t` in the 3rd equation and solve for `c`:

`c + a + t = 430` becomes:

`c + c/3 + c + 10 = 430`

`(3/3 xx c) + c/3 + (3/3 xx c) + 10 = 430`

`(3c)/3 + c/3 + (3c)/3 + 10 = 430`

`(3c)/3 + (1c)/3 + (3c)/3 + 10 = 430`

`((3 + 1 + 3)c)/3 + 10 = 430`

`(7c)/3 + 10 = 430`

`(7c)/3 + 10 - color(red)(10) = 430 - color(red)(10)`

`(7c)/3 + 0 = 420`

`(7c)/3 = 420`

`color(red)(3)/color(blue)(7) xx (7c)/3 = color(red)(3)/color(blue)(7) xx 420`

`cancel(color(red)(3))/cancel(color(blue)(7)) xx (color(blue)(cancel(color(black)(7)))c)/color(red)(cancel(color(black)(3))) = color(red)(3)/cancel(color(blue)(7)) xx color(blue)(cancel(color(black)(420)))60`

`c = 180`

Carlos gained 180 yards