QuestionAugust 26, 2025

5. For how many games is the total cost of bowling equal for the two bowling est blishments?

5. For how many games is the total cost of bowling equal for the two bowling est blishments?
5.
For how many games is the total cost of bowling equal for the two bowling
est blishments?

Solution
4.1(364 votes)

Answer

x = \frac{d - b}{a - c} games Explanation 1. Define the cost equations Let C_1 = a \cdot x + b and C_2 = c \cdot x + d, where x is the number of games, a and c are per game costs, and b and d are fixed costs. 2. Set the equations equal Solve a \cdot x + b = c \cdot x + d for x. 3. Rearrange terms Rearrange to a \cdot x - c \cdot x = d - b. 4. Factor and solve for x Factor to (a - c) \cdot x = d - b. Solve for x: x = \frac{d - b}{a - c}.

Explanation

1. Define the cost equations<br /> Let $C_1 = a \cdot x + b$ and $C_2 = c \cdot x + d$, where $x$ is the number of games, $a$ and $c$ are per game costs, and $b$ and $d$ are fixed costs.<br />2. Set the equations equal<br /> Solve $a \cdot x + b = c \cdot x + d$ for $x$.<br />3. Rearrange terms<br /> Rearrange to $a \cdot x - c \cdot x = d - b$.<br />4. Factor and solve for x<br /> Factor to $(a - c) \cdot x = d - b$. Solve for $x$: $x = \frac{d - b}{a - c}$.
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