Question

Solve this application problem using a system of equations: The Bright College footballteam scored 80 times last season, some on seven-point touchdowns and some on three-point field goals. The 80 scores accounted for 516 points. How many touchdowns and field goals did they score

Answer 1

`\large \boxed{\sf \ \ 69 \ \textbf{touchdowns } 11 \ \textbf{field goals } \ }`

Explanation:

Hello,

Touchdown is 7 points, field goals is 3 points

Let's note a the number of touchdowns and b the number of field goals, we can write

(1) a + b = 80

(2) 7a + 3b = 516

(2) - 3*(1) gives

7a + 3b - 3(a + b) = 516 - 3*80

<=> 7a + 3b -3a - 3b = 516 - 240 = 276

<=> 4a = 276

<=>
`a=(276)/(4)=69`

And then from (1) b = 80 - 69 = 11

Hope this helps