Question

Julie orders three scoops of ice cream and a drink and pays $4.46. Carrie orders two scoops of ice cream and a drink and pays $3.57. If Samantha only wants a drink but decides to supersize it for an additional $0.50, how much does she pay?

(Note: Assume there is no sales tax.)

Answer 1

Let's denote the cost of one scoop of ice cream as \( x \) and the cost of a drink as \( y \).

From the information given:

1. Julie orders three scoops of ice cream and a drink for a total of $4.46:
\[
3x + y = 4.46
\]

2. Carrie orders two scoops of ice cream and a drink for a total of $3.57:
\[
2x + y = 3.57
\]

To solve these equations, we can eliminate \( y \) by subtracting the second equation from the first:

\[
(3x + y) - (2x + y) = 4.46 - 3.57
\]

This simplifies to:

\[
3x - 2x = 4.46 - 3.57
\]
\[
x = 0.89
\]

Now that we have the cost of one scoop of ice cream, we can substitute \( x \) back into one of the original equations to find \( y \). We can use the second equation:

\[
2(0.89) + y = 3.57
\]
\[
1.78 + y = 3.57
\]
\[
y = 3.57 - 1.78
\]
\[
y = 1.79
\]

Now we have determined that the cost of one scoop of ice cream is \( x = 0.89 \) and the cost of a drink is \( y = 1.79 \).

Samantha wants only a drink and decides to supersize it for an additional \( 0.50 \). The cost of the drink including the supersizing is:

\[
\text{Total cost} = y + 0.50 = 1.79 + 0.50 = 2.29
\]

Thus, the amount Samantha pays is \( \boxed{2.29} \).