To find out how much money was on the gift card when Nevaeh received it, we need to identify the amount of money remaining at the start (when no coffee has been purchased) and see how the money changes as cups of coffee are bought.
From the provided data:
- 3 cups of coffee: $21 remaining
- 4 cups of coffee: $18 remaining
- 6 cups of coffee: $12 remaining
- 8 cups of coffee: $6 remaining
To find the initial amount on the gift card, we can deduce that the cost of each cup of coffee is constant. We can calculate the cost of coffee by finding the difference in the amount remaining as the number of cups increases.
For example:
-
From 3 cups to 4 cups: \[ 21 - 18 = 3 \quad (cost of 1 cup of coffee) \]
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From 4 cups to 6 cups: \[ 18 - 12 = 6 \quad (cost of 2 cups of coffee = 3 \text{ each} \times 2 = 6) \]
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From 6 cups to 8 cups: \[ 12 - 6 = 6 \quad (cost of 2 cups of coffee = 3 \text{ each} \times 2 = 6) \]
So, we can confirm that each cup of coffee costs $3.
Now, we can look at the number of cups of coffee purchased and the remaining amount to find out the total initial amount:
Let \( r \) be the number of cups, and let \( y \) be the money remaining.
To express the remaining money in terms of the initial amount \( M \): \[ y = M - 3r \]
We can use any of the points given. Let's use the point with 3 cups of coffee remaining $21: \[ 21 = M - 3(3) \] \[ 21 = M - 9 \] \[ M = 21 + 9 \] \[ M = 30 \]
Thus, the initial amount on the gift card when Nevaeh received it was $30.