Question

In the 2000-2001 season, Minnesota’s Katie Smith was ranked first in the WNBA for total points and three-point field goals made. She scored 646 points making 355 shots, including 3-point field goals, 2-point field goals, and 1-point free throws. She made 27 more 2-point field goals than 3- point field goals.

Write a system of three equations that represents the number of goals Katie Smith made.

Short answer

The required system of three equations is

$\begin{array}{d}x+y+z=355\\ x+2y+3z=646\\ y-z=27\end{array}$

Step-by-step solution

– First construct the equations corresponding to the given situation.

Let $x$be the number of 1-point free throws, $y$be the number of 2-point field goals, and $z$be the number of 3-point field goals.

In the figure, it is given that the total 355 shots are made.

So, localid="1647999230722" $x+y+z=355$.

In the figure, it is given that the total scored points is 646.

So, $x+2y+3z=646$

In the figure, it is given that the 27 more 2-point field goals than 3-point field goals.

This can be mathematically written as $y=z+27\Rightarrow y-z=27$.

x+y+z=355x+2y+3z=646y−z=27Step 2 – Write the equations as a system of three equations.

So, the system of equations will be: