`50t+3c=300`
Robert is playing blackjack at a casino. The equation above can be used to model the number of chips, c, that Robert still has in his possession t hours after he begins playing. What does it mean that `t=0, c=100` is a solution to this equation?
(A) Robert is losing 10 chips per hour.
(B) It would take 100 hours for robert to have 300 chips.
(C) Robert can play for 100 hours before losing all his chips.
(D) Robert begins playing with 100 chips.

Options

A. Robert is losing 10 chips per hour.
B. It would take 100 hours for Robert to have 300 chips.
C. Robert can play for 100 hours before losing all his chips.
D. Rober beings playing with 100 chips.

Answer

To solve the problem, we start with the given equation:

\[ 50t + 3c = 300 \]

We need to analyze what it means for the point \( t = 0 \) and \( c = 100 \) to be a solution to this equation.

### Step 1: Substitute \( t = 0 \) and \( c = 100 \) into the equation

We substitute \( t = 0 \) and \( c = 100 \) into the equation:

\[ 50(0) + 3(100) = 300 \]

### Step 2: Simplify the equation

Now, we simplify the left-hand side:

\[ 0 + 300 = 300 \]

This simplifies to:

\[ 300 = 300 \]

### Step 3: Interpret the result

Since the equation holds true, it confirms that \( t = 0 \) and \( c = 100 \) is indeed a solution. This means that at the moment the game starts (when \( t = 0 \)), Robert has 100 chips.

### Step 4: Analyze the meaning of the solution

The solution \( t = 0, c = 100 \) indicates that Robert begins playing with 100 chips. This directly corresponds to option D in the multiple-choice answers.

### Conclusion

Thus, the correct interpretation of the solution \( t = 0, c = 100 \) is:

**(D) Robert begins playing with 100 chips.**

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