`7x+y=133`
Jaffrey has set a monthly budget for purchasing frozen blended mocha drinks from his local SpendBucks coffee shop. The equations above can be used to model amount of his budget, y, in dollars that remains after buying coffee for x days in a month. What does it mean that (19.0) is a solution to this equation?

Options

A. Jeffrey starts the month with a budget of $19.
B. Jeffrey spends $19 on coffee every day.
C. It takes 19 days for Jeffrey to drink 133 cups of coffee.
D. It takes 19 days for Jeffrey to run out of money in his budget for purchsing coffee.

Answer

To solve the problem, we need to analyze the equation given and interpret what it means when (19, 0) is a solution to this equation.

### Step-by-Step Solution:

1. **Understand the Equation**: The equation given is \(7x + y = 133\). Here, \(x\) represents the number of days Jaffrey buys coffee, and \(y\) represents the amount of budget left after buying coffee for \(x\) days.

2. **Substitute the Solution**: We are given the solution (19, 0). This means we will substitute \(x = 19\) and \(y = 0\) into the equation:
\[ 7(19) + 0 = 133 \]

3. **Calculate**: Now, calculate \(7(19)\):
\[ 7 \times 19 = 133 \]
Therefore, substituting back into the equation gives:
\[ 133 + 0 = 133 \]
This confirms that the point (19, 0) satisfies the equation.

4. **Interpret the Result**: Since we found that when \(x = 19\), \(y = 0\), this means that after buying coffee for 19 days, Jaffrey has spent all of his budget. Thus, he has $0 left after 19 days.

5. **Conclusion**: The solution (19, 0) indicates that it takes Jaffrey 19 days to completely exhaust his budget of $133 when he spends a certain amount each day.