Question

Leo had a $30 gift card to use at a coffee shop. He used the entire balance to buy regular-sized coffees, which cost $2, and large coffees, which cost $3. If he bought 13 coffees in total, how many large coffees did he buy?
2
3
4
9

Answer 1

Let \( r \) represent the number of regular-sized coffees Leo bought and \( l \) represent the number of large coffees he bought. We can set up the following equations based on the information given:

1. The total number of coffees purchased:
\[
r + l = 13
\]

2. The total cost of the coffees purchased:
\[
2r + 3l = 30
\]

Now, we can solve these equations step by step. From the first equation, we can express \( r \) in terms of \( l \):
\[
r = 13 - l
\]

Next, we substitute this expression for \( r \) into the second equation:
\[
2(13 - l) + 3l = 30
\]

Now, distribute the 2:
\[
26 - 2l + 3l = 30
\]

Combine the \( l \) terms:
\[
26 + l = 30
\]

Now, isolate \( l \):
\[
l = 30 - 26
\]
\[
l = 4
\]

Therefore, Leo bought \( \boxed{4} \) large coffees.

To verify:
If \( l = 4 \), then:
\[
r = 13 - 4 = 9
\]
Calculating the total cost:
\[
2r + 3l = 2(9) + 3(4) = 18 + 12 = 30
\]
The calculations are correct, confirming that the answer is indeed \( \boxed{4} \).