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Difference between revisions of "2014 AMC 10A Problems/Problem 3"

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==Solution==
 
==Solution==
<math>\dfrac{1}{2}</math> of the bread is <math>24</math> loaves. <math>24\times\textdollar 2.50=\textdollar60</math>. This leaves <math>24</math> loaves left.
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She first sells one-half of her <math>48</math> loaves, or <math>\frac{48}{2}=24</math> loaves. Each loaf sells for <math>\textdollar 2.50</math>, so her total earnings in the morning is equal to <cmath>24\cdot \textdollar 2.50 = \textdollar 60</cmath>
  
<math>\dfrac{2}{3}\times 24=16</math> The new price will be <math>\dfrac{1}{2}\textdollar2.50=\textdollar1.25</math>. So  <math>\textdollar1.25\times16=\textdollar20.00</math>. This leaves 8 loaves remaining.
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This leaves 24 loaves left, and Bridget will sell <math>\dfrac{2}{3}\times 24=16</math> of them for a price of <math>\textdollar\frac{2.50}{2}=\textdollar 1.25</math>. Thus, her total earnings for the afternoon is <cmath>16\cdot \textdollar 1.25 = \textdollar 20</cmath>
  
We have <math>\textdollar 1\times 8=\textdollar 8.00</math>.
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Finally, Bridget will sell the remaining <math>24-16=8</math> loaves for a dollar each. This is a total of <math>\textdollar 1\cdot 8 = \textdollar 8</math>
  
The total amount of money she made for the day is the sum of these amounts, which is <math>60+20+8=\textdollar 88</math>.
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The total amount of money she makes is equal to <math>60+20+8=\textdollar 88</math>.
  
The total amount it cost her to make all of the loaves is <math>\textdollar 0.75*48=\textdollar 36</math>.
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However, since Bridget spends <math>\textdollar 0.75</math> making each loaf of bread, the total cost to make the bread is equal to  <math>\textdollar 0.75\cdot48=\textdollar 36</math>.
  
Therefore, her total profit is the amount of money she spent subtracted from the amount of money she made. <math>88-36=52\implies\boxed{\textbf{(E)}52}}</math>.
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Her total profit is the amount of money she spent subtracted from the amount of money she made, which is <cmath>88-36=52\implies\boxed{\textbf{(E)} \ 52}}</cmath>
  
 
==See Also==
 
==See Also==

Revision as of 10:29, 9 February 2014

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. ! Extra }, or forgotten $.)

Solution

She first sells one-half of her $48$ loaves, or $\frac{48}{2}=24$ loaves. Each loaf sells for $\textdollar 2.50$, so her total earnings in the morning is equal to \[24\cdot \textdollar 2.50 = \textdollar 60\]

This leaves 24 loaves left, and Bridget will sell $\dfrac{2}{3}\times 24=16$ of them for a price of $\textdollar\frac{2.50}{2}=\textdollar 1.25$. Thus, her total earnings for the afternoon is \[16\cdot \textdollar 1.25  = \textdollar 20\]

Finally, Bridget will sell the remaining $24-16=8$ loaves for a dollar each. This is a total of $\textdollar 1\cdot 8 = \textdollar 8$

The total amount of money she makes is equal to $60+20+8=\textdollar 88$.

However, since Bridget spends $\textdollar 0.75$ making each loaf of bread, the total cost to make the bread is equal to $\textdollar 0.75\cdot48=\textdollar 36$.

Her total profit is the amount of money she spent subtracted from the amount of money she made, which is

\[88-36=52\implies\boxed{\textbf{(E)} \ 52}}\] (Error compiling LaTeX. ! Extra }, or forgotten $.)

See Also

2014 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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