Q 87 - Intermediate Algebra

Question

Drew burned $1800$ calories Friday playing one hour of basketball and canoeing for two hours. Saturday he spent two hours playing basketball and three hours canoeing and burned
$3200$ calories. How many calories did he burn per hour when playing basketball? How many calories did he burn per hour when canoeing?

Step-by-Step Solution

Answer

The number of calories that Drew burned while playing basketball is $1000$ and the number of calories he burned while canoeing is $400$

Step 1. Given

Drew burned $1800$ calories by playing $1$ hour of basketball and $2$ hours of canoeing.

And he burned $3200$ calories by playing $2$ hours of basketball and $3$ hours of canoeing.

Step 2. Form the linear equations

Let $x$ denote the number of calories burned by Drew by playing basketball.

And $y$ denote the number of calories burned by playing canoeing.

Drew burned $1800$ calories by playing $1$ hour in basketball and two hour in canoeing.

So, $x+2y=1800$

He burned $3200$ calories by playing $2$ hour in basketball and $3$ hour in canoeing

So, $2x+3y=3200$

Step 3. Solve the linear equations

Solve the system of linear equations.

  $x+2y=1800$

$2x+3y=3200$

Solve the first equation for $x$,

          $x=1800-2y$

Step 4. Solve for y

Substitute $x=1800-2y$ in the second equation,

                 $2x+3y=3200$

$2(1800-2y)+3y=3200$

     $3600-4y+3y=3200$

               $3600-y=3200$

                           $y=3600-3200$

                           $y=400$

The number of calories burned by Drew by playing Canoeing is $400$ calories.

Step 5. Solve for x

Substitute $y=400$ in the first equation, we get,

          $x+2y=1800$

   $x+2\left(400\right)=1800$

        $x+800=1800$

                  $x=1800-800$

                  $x=1000$

The number of calories burned by Drew by playing basketball is $1000$

Step 6. Check the answer

Substitute $x=1000$,

                  $y=400$ in the first equation,

                $x+2y=1800$

$\left(1000\right)+2\left(400\right)=1800$

       $1000+800=1800$

                 $1800=1800$

Hence the equation holds true.