Question

gretchen is a member of levelup pass video game online store, which has two payment plans: - no plan, with a cost of $28 per game - premium plan, with an enrollment fee of $150 and a cost of $13 per game question 5: what is the number of games where the cost of no plan and a premium plan are the same (known as the \breakeven point\)? question 6: if gretchen expects to download 7 games, which plan should she choose?

Explanation:

Step1: Define cost equations

Let $x$ = number of games.
No plan cost: $C_1 = 28x$
Premium plan cost: $C_2 = 150 + 13x$

Step2: Find breakeven point

Set $C_1 = C_2$:
$28x = 150 + 13x$

Step3: Solve for $x$

Subtract $13x$ from both sides:
$28x - 13x = 150$
$15x = 150$
$x = \frac{150}{15} = 10$

Step4: Calculate cost for 7 games

No plan cost: $C_1 = 28 \times 7 = 196$
Premium plan cost: $C_2 = 150 + 13 \times 7 = 150 + 91 = 241$

Step5: Compare costs for 7 games

$196 < 241$, so no plan is cheaper.

Answer:

Question 5: 10
Question 6: No plan