Question

5
systems of equations: word problem practice
objective: use the desmos graphing calculator to solve these real - world scenarios. for the first five, the equations are provided. for the last five, you must write the equations before graphing.
the school car wash the junior class is washing cars. they spent $100 on supplies and charge $5 per car, so their profit is $p = 5n - 100$. the senior class spent $20 on supplies and charges $3 per car ($p = 3n - 20$). how many cars ($n$) must each wash to have the same profit ($p$)? equations: $y = 5x - 100$ and $y = 3x - 20$

Explanation:

Step1: Set the two profit equations equal

Since we want the profits to be the same, we set \(5n - 100 = 3n - 20\).

Step2: Solve for \(n\)

Subtract \(3n\) from both sides: \(5n - 3n - 100 = 3n - 3n - 20\) which simplifies to \(2n - 100 = -20\).
Then add 100 to both sides: \(2n - 100 + 100 = -20 + 100\) giving \(2n = 80\).
Divide both sides by 2: \(\frac{2n}{2}=\frac{80}{2}\) so \(n = 40\).

Answer:

40