# 2014 AMC 10A Problems/Problem 3

## Problem

Bridget bakes 48 loaves of bread for her bakery. She sells half of them in the morning for $\textdollar 2.50$ each. In the afternoon she sells two thirds of what she has left, and because they are not fresh, she charges only half price. In the late afternoon she sells the remaining loaves at a dollar each. Each loaf costs $\textdollar 0.75$ for her to make. In dollars, what is her profit for the day?

$\textbf{(A)}\ 24\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 44\qquad\textbf{(D)}}\ 48\qquad\textbf{(E)}\ 52$ (Error compiling LaTeX. )

## Solution

$\dfrac{1}{2}$ of the bread is $24$ loaves. $24\times\textdollar 2.50=\textdollar60$. This leaves $24$ loaves left.

$\dfrac{2}{3}\times 24=16$ The new price will be $\dfrac{1}{2}\textdollar2.50=\textdollar1.25$. So $\textdollar1.25\times16=\textdollar20.00$. This leaves 8 loaves remaining.

We have $\textdollar 1\times 8=\textdollar 8.00$.

The total amount of money she made for the day is the sum of these amounts, which is $60+20+8=\textdollar 88$.

The total amount it cost her to make all of the loaves is $\textdollar 0.75*48=\textdollar 36$.

Therefore, her total profit is the amount of money she spent subtracted from the amount of money she made. $88-36=52\implies\boxed{\textbf{(E)}52}}$ (Error compiling LaTeX. ).