Q10. - Algebra 1

Question

In football, a field goal is worth 3 points, and the extra point after a touchdown is worth 1 point. During the 2006 season, John Kasay of the Carolina Panthers scored a total of 100 points for his team by making a total of 52 field goals and extra points. How many field goals did he make?

Step-by-Step Solution

Answer

John Kasay scored 24 field goals.

Step 1.State the concept of substitution method in system of linear equation with two unknown.

The method of solving the system of linear equations with two unknown, by writing any one equation in terms of one variable and substituting that value in other equation to remove one unknown(variable) from the equation.

By removing one variable from the equation it is easy to find the value of other variable by simplifying the equation.

Step 2. Write the two equations.

Let ‘$x$’ be the number of field goals and ‘$y$’ be the total number of extra points.

A field goal is worth 3 points.

Therefore, total points for $x$ goals$=3x$ points.

From the $1^{st}$ condition,

John Kasay of the Carolina Panthers scored a total of 100 points by field goals and extra points.

 $3x+y=100 \dots \left(1\right)$

From the $2^{nd}$ condition,

John Kasay of the Carolina Panthers scored a total of 52 field goals and extra points.

$x+y=52 \dots \left(2\right)$

Step 3. Calculate the number of filed goals.

Solve equation $\left(1\right) \& \left(2\right)$ using substitution method and find the value of $x$.

From $\left(2\right)$,

$\begin{array}{l}x+y=52\\ y=52-x\end{array}$

Substitute $y=52-x$ in $\left(1\right)$ and simplify further.

$\begin{array}{l}3x+y=100\\ 3x+(52-x)=100\\ 3x+52-x=100\\ 3x-x+52=100\\ 2x=100-52\\ 2x=48\\ \frac{2x}{x}=\frac{48}{2}\\ x=24\end{array}$

Therefore, John Kasay scored 24 field goals.