A baker baked 30% more loaves of sourdough bread on Saturday than on Friday. If the average number of sourdough loaves baked across these two days was 115, how many loaves did the baker make on Friday?

The correct answer is 100.

Step-by-Step Solution:

Step 1: Define the variable.
Let $x$ represent the number of sourdough bread loaves baked on Friday.

Step 2: Express the number of loaves baked on Saturday.
The baker baked 30% more loaves on Saturday than on Friday. Therefore, the number of loaves baked on Saturday is:

$\text{Saturday's loaves}=x+0.30x=1.30x$

Step 3: Set up the equation for the average.
The average number of loaves baked across the two days is 115. The formula for the average is:

$\text{Average}=\frac{\text{Friday's loaves}+\text{Saturday's loaves}}{2}$

Substitute the expressions in terms of $x$:

$115=\frac{x+1.30x}{2}$

$115=\frac{2.30x}{2}$

$115=1.15x$

Step 4: Solve for $x$.
Divide both sides by 1.15:

$x=\frac{115}{1.15}$

$x=100$

Thus, the baker baked 100 loaves of sourdough bread on Friday.