Q 4.31 - Intermediate Algebra

Question

Translate to a system of equations and then solve:

Mark went to the gym and did $40$ minutes of Bikram hot yoga and $10$ minutes of jumping jacks. He burned $510$ calories. The next time he went to the gym, he did $30$ minutes of Bikram hot yoga and $20$ minutes of jumping jacks burning $470$ calories. How many calories were burned for each minute of yoga? How many calories were burned for each minute of jumping jacks?

Step-by-Step Solution

Answer

The amount of calories burnt per minute for doing Bikram hot yoga and jumping jacks are $11$ and $7$ calories respectively.

Step 1 . Given

We are given that Mark burn $510$ calories for doing $40$ minutes of Bikram hot yoga and $10$ minutes of jumping jacks and for doing $30$ minutes of Bikram hot yoga and $20$ minutes of jumping jacks he burns $470$ calories.

Step 2 . Explanation and Assumptions.

Let $x$ be the calories burn per minute for doing Bikram hot yoga and $y$ be the calories burn per minute for doing jumping jacks.

The equations representing the calories burned are,

$$\begin{gathered} 40x+10y=510 \\ 30x+20y=470 \end{gathered}$$

Step 3. Solving the equations.

Multiplying $2$ in the first equation, we get

$$\begin{gathered} 2(40x+10y)=2\times 510 \\ 80x+20y=1020 \end{gathered}$$

Now, Subtracting the equations, we get

$50x=550$

Dividing by $50$, we get

$x=11$

Step 4. Finding y by putting the value of x .

Putting the value of $x$ in second equation, we get

$$\begin{gathered} 30\times 11+20y=470 \\ 330+20y=470 \\ 20y=470-330 \\ 20y=140 \end{gathered}$$

Dividing by $20$, we get

$y=7$

Step 4. Checking the solution

Checking the solution by putting the value of $x,y$ in the equations, we get

$$\begin{gathered} 40x+10y=510 \\ 40\left(11\right)+10\left(7\right)=510 \\ 440+70=510 \\ 510=510 \\ 30x+20y=470 \\ 30\left(11\right)+20\left(7\right)=470 \\ 330+140=470 \\ 470=470 \end{gathered}$$

This is true, hence the solution is correct.