Question

Logan and Zoey went out to dinner. Zoey's dinner bill was $5 more than half of Logan's bill. If the total of the two bills combined was $60.26, what was Zoey's dinner bill? Logan's?

Answer 1

Let's denote Logan's dinner bill as \( L \) and Zoey's dinner bill as \( Z \).

From the problem, we know two things:
1. Zoey's bill was $5 more than half of Logan's bill, which can be expressed as:
\[
Z = \frac{1}{2}L + 5
\]
2. The total of the two bills combined was $60.26, which can be expressed as:
\[
L + Z = 60.26
\]

Now, we can substitute the first equation into the second. Replacing \( Z \) in the total equation gives us:
\[
L + \left(\frac{1}{2}L + 5\right) = 60.26
\]

Now, combine like terms:
\[
L + \frac{1}{2}L + 5 = 60.26
\]
\[
\frac{3}{2}L + 5 = 60.26
\]

Next, subtract 5 from both sides:
\[
\frac{3}{2}L = 60.26 - 5
\]
\[
\frac{3}{2}L = 55.26
\]

Now, multiply both sides by \(\frac{2}{3}\) to solve for \( L \):
\[
L = \frac{2}{3} \times 55.26
\]
\[
L = \frac{110.52}{3}
\]
\[
L = 36.84
\]

Now that we have \( L \), we can find \( Z \) using the first equation:
\[
Z = \frac{1}{2}L + 5
\]
\[
Z = \frac{1}{2} \times 36.84 + 5
\]
\[
Z = 18.42 + 5
\]
\[
Z = 23.42
\]

Thus, the final amounts are:
- Logan's dinner bill: **$36.84**
- Zoey's dinner bill: **$23.42**