Question

3 numeric 2 points charles is comparing two different family membership plans to the zoo. each plan charges a fixed fee and a price per person. the system of equations shows the total cost, y, for x family members. \\(\

$$\begin{cases} y = 20x + 15 \\\\ y = 15x + 30 \\end{cases}$$

\\) for how many family members will the cost be the same? answer

Explanation:

Step1: Set equations equal (costs same)

Since $y$ represents total cost, set the two expressions for $y$ equal to each other:
$20x + 15 = 15x + 30$

Step2: Isolate x terms

Subtract $15x$ from both sides:
$20x - 15x + 15 = 30$
$5x + 15 = 30$

Step3: Isolate constant terms

Subtract 15 from both sides:
$5x = 30 - 15$
$5x = 15$

Step4: Solve for x

Divide both sides by 5:
$x = \frac{15}{5}$

Answer:

3