Difference between revisions of "2014 AMC 10A Problems/Problem 3"
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Bridget bakes 48 loaves of bread for her bakery. She sells half of them in the morning for <math>\textdollar 2.50</math> 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 <math>\textdollar 0.75</math> for her to make. In dollars, what is her profit for the day? | Bridget bakes 48 loaves of bread for her bakery. She sells half of them in the morning for <math>\textdollar 2.50</math> 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 <math>\textdollar 0.75</math> for her to make. In dollars, what is her profit for the day? | ||
| − | <math>\textbf{(A)}\ 24\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 44\qquad\textbf{(D) | + | <math>\textbf{(A)}\ 24\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 44\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 52</math> |
==Solution== | ==Solution== | ||
| − | <math> | + | 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> | + | 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> |
| − | + | 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 | + | The total amount of money she makes is equal to <math>60+20+8=\textdollar 88</math>. |
| − | + | 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>. | |
| − | + | 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> | |
| + | |||
| + | ==Video Solution (CREATIVE THINKING)== | ||
| + | https://youtu.be/Lr5GAX8vFcU | ||
| + | |||
| + | ~Education, the Study of Everything | ||
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| + | |||
| + | |||
| + | |||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/0RWz4LBYFGM | ||
| + | |||
| + | ~savannahsolver | ||
==See Also== | ==See Also== | ||
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{{AMC10 box|year=2014|ab=A|num-b=2|num-a=4}} | {{AMC10 box|year=2014|ab=A|num-b=2|num-a=4}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
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| + | [[Category: Prealgebra Problems]] | ||
Latest revision as of 23:11, 26 June 2023
Problem
Bridget bakes 48 loaves of bread for her bakery. She sells half of them in the morning for 
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 
for her to make. In dollars, what is her profit for the day?
Solution
She first sells one-half of her 
loaves, or 
loaves. Each loaf sells for , so her total earnings in the morning is equal to ![\[24\cdot \textdollar 2.50 = \textdollar 60\]](http://latex.artofproblemsolving.com/d/1/a/d1a73555236ea88d2364ec2a9f5ec4e28dba4770.png)
This leaves 24 loaves left, and Bridget will sell 
of them for a price of 
. Thus, her total earnings for the afternoon is ![\[16\cdot \textdollar 1.25 = \textdollar 20\]](http://latex.artofproblemsolving.com/e/5/4/e54a88612e076fcbb746749cde7ab567cc303e23.png)
Finally, Bridget will sell the remaining 
loaves for a dollar each. This is a total of 
The total amount of money she makes is equal to 
.
However, since Bridget spends making each loaf of bread, the total cost to make the bread is equal to 
.
Her total profit is the amount of money she spent subtracted from the amount of money she made, which is ![\[88-36=52\implies\boxed{\textbf{(E)} \ 52}\]](http://latex.artofproblemsolving.com/4/a/0/4a085907343e46e4b1b8c80afdb3cc746896b312.png)
Video Solution (CREATIVE THINKING)
https://youtu.be/Lr5GAX8vFcU
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 2014 AMC 10A (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
