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

Revision as of 01:45, 7 December 2024

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?

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

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 $88-36=52\implies\boxed{\textbf{(E)} \ 52}$

Solution 2

As we know inherently from the information provided above that B bakes $48$ loaves. We know that she sells $\frac{1}{2}$ of the loaves for $$$$ 2.50 $each, and she sells half of them, so we multiply$ 24 $by$ $ $2.50$ , which equals $$$$ 60 $. For the two thirds left, or$ 16 $loaves remaining, she sells them for$ $ $1.25$ , so we multiply $$$$ 1.25 $by$ 16 $, which equals$ $ $20$ . Finally, she sells the remaining, she sells the loaves at $$$$ 1 $dollar each, for the$ 8 $remaining loaves. We multiply$ $ $1$ by $8$ to get $$$$ 8 $, so in total, she makes$ $ $84$ . However, we have to consider the fact that it takes her $$$$ 0.75 $to make a loaf. We multiply that number by the total number of loaves, which is$ 48 $, so$ $ $0.75 \times 48 =$ 36 $. Subtract$ $ $36$ from $$$$ 84 $, we get the final answer of$ $ $48$ profit.

~Horizon

Video Solution (CREATIVE THINKING)

https://youtu.be/Lr5GAX8vFcU

~Education, the Study of Everything

Video Solution

https://youtu.be/0RWz4LBYFGM

~savannahsolver

@@ Line 19: / Line 19: @@
 ==Solution 2==
-As we know inherently from the information provided above that B bakes <math>48</math> loaves. We know that she sells <math>\frac{1}{2}=</math> of the loaves for <math></math>2.50<math> each, and she sells half of them, so we multiply </math>24<math> by </math><math>2.50</math>, which equals <math></math>60<math>. For the two thirds left, or </math>16<math> loaves remaining, she sells them for </math><math>1.25</math>, so we multiply <math></math>1.25<math> by </math>16<math>, which equals </math><math>20</math>. Finally, she sells the remaining, she sells the loaves at <math></math>1<math> dollar each, for the </math>8<math> remaining loaves. We multiply </math><math>1</math> by <math>8</math> to get <math></math>8<math>, so in total, she makes </math><math>84</math>. However, we have to consider the fact that it takes her <math></math>0.75<math> to make a loaf. We multiply that number by the total number of loaves, which is 48, so </math><math>0.75</math> * 48 = <math></math>36<math>. Subtract </math><math>36</math> from <math></math>84<math>, we get the final answer of </math><math>48</math> profit.
+As we know inherently from the information provided above that B bakes <math>48</math> loaves. We know that she sells <math>\frac{1}{2}</math> of the loaves for <math>\$</math>2.50<math> each, and she sells half of them, so we multiply </math>24<math> by </math>\$<math>2.50</math>, which equals <math>\$</math>60<math>. For the two thirds left, or </math>16<math> loaves remaining, she sells them for </math>\$<math>1.25</math>, so we multiply <math>\$</math>1.25<math> by </math>16<math>, which equals </math>\$<math>20</math>. Finally, she sells the remaining, she sells the loaves at <math>\$</math>1<math> dollar each, for the </math>8<math> remaining loaves. We multiply </math>\$<math>1</math> by <math>8</math> to get <math>\$</math>8<math>, so in total, she makes </math>\$<math>84</math>. However, we have to consider the fact that it takes her <math>\$</math>0.75<math> to make a loaf. We multiply that number by the total number of loaves, which is </math>48<math>, so </math>\$<math>0.75 \times 48 = \$</math>36<math>. Subtract </math>\$<math>36</math> from <math>\$</math>84<math>, we get the final answer of </math>\$<math>48</math> profit.
 ~Horizon

2014 AMC 10A (Problems • Answer Key • Resources)
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