Question

3 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 video game subscription two brothers are saving money. liam starts with $50 and saves $15 a week ($y = 15x + 50$). noah starts with nothing but saves $25 a week ($y = 25x$). when will they have the same amount of money?
equations: $y = 15x + 50$ and $y = 25x$

Explanation:

Step1: Set the two equations equal

Since we want to find when they have the same amount of money, we set \( y = 15x + 50 \) equal to \( y = 25x \). So we get the equation \( 15x + 50 = 25x \).

Step2: Solve for x

Subtract \( 15x \) from both sides of the equation: \( 15x + 50 - 15x = 25x - 15x \), which simplifies to \( 50 = 10x \). Then divide both sides by 10: \( \frac{50}{10}=\frac{10x}{10} \), so \( x = 5 \).

Answer:

After 5 weeks, they will have the same amount of money.