Q29. - Algebra 2

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.

Step-by-Step Solution

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 1 – 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, $x+y+z=355$.

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

So, the system of equations will be: