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?

NOTE: Type the numerical value into each box to receive credit. Do NOT type the $ into the box, or it will be counted incorrect.

(2 points)
Zoey's Bill: $

Logan's Bill: $

Answer 1

Let's denote Logan's bill as \( L \) and Zoey's bill as \( Z \). According to the problem, we have the following two equations:

1. \( Z = \frac{1}{2}L + 5 \) (Zoey's bill is $5 more than half of Logan's bill)
2. \( L + Z = 60.26 \) (The total of their bills is $60.26)

Now, we can substitute the expression for \( Z \) from the first equation into the second equation:

\[
L + \left(\frac{1}{2}L + 5\right) = 60.26
\]

Combining like terms, we get:

\[
L + \frac{1}{2}L + 5 = 60.26
\]

This simplifies to:

\[
\frac{3}{2}L + 5 = 60.26
\]

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 \( L \):

\[
L = \frac{2}{3} \times 55.26
\]

Calculating this gives:

\[
L = 36.84
\]

Now that we have Logan's bill, we can find Zoey's bill using the first equation:

\[
Z = \frac{1}{2}L + 5
\]

Substituting \( L = 36.84 \):

\[
Z = \frac{1}{2} \times 36.84 + 5
\]

Calculating this:

\[
Z = 18.42 + 5 = 23.42
\]

So, Logan's bill is $36.84 and Zoey's bill is $23.42.

The final answers are:

Zoey's Bill: 23.42
Logan's Bill: 36.84