# Question #3dc62

Jun 22, 2017

$\text{elliptical"=16 " }$ and $\text{ ""treadmill} = 32$

#### Explanation:

Let $l$ be the number of minutes you spend on the elliptical, and $t$ be the number of minutes you spend on the treadmill.

We can make 2 equations:

We know that the total number of minutes is 48, so:

$l + t = 48$

We know that the total calorie burn must be 400, so:

$9 l + 8 t = 400$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now that we have a system of equations, we can solve it through subtraction, like this:

Multiply both sides of the first equation by $8$:

$8 l + 8 t = 384$

Now subtract this modified form of the first equation from the second equation:

$\textcolor{w h i t e}{\text{X..}} 9 l + 8 t = 400$
$- \left(8 l + 8 t = 384\right)$
$- - - - - - -$

$\textcolor{w h i t e}{\text{XXXXX}} l = 16$

So we know what $l$ is. To find what $t$ is, we need to plug $l$ back into one of the equations and solve for $t$:

$l + t = 48$

$16 + t = 48$

$t = 32$

So $l = 16$ and $t = 32$.