Difference between revisions of "1953 AHSME Problems/Problem 1"

 
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==Solution 2==
 
==Solution 2==
The boy buys <math>3</math> oranges for <math>10</math> cents. He sells them at <math>5</math> for <math>20</math>. So, he buys <math>15</math> for <math>50</math> cents and sells them a <math>15</math> for <math>60</math> cents, so he makes <math>10</math> cents of profit on every <math>5</math> oranges. To make <math>100</math> cents of profit, he needs to sell <math>10\cdot 5</math>, or <math>50</math> oranges.
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The boy buys <math>3</math> oranges for <math>10</math> cents. He sells them at <math>5</math> for <math>20</math> cents. So, he buys <math>15</math> for <math>50</math> cents and sells them at <math>15</math> for <math>60</math> cents, so he makes <math>10</math> cents of profit on every <math>15</math> oranges. To make <math>100</math> cents of profit, he needs to sell <math>15 \cdot \frac{100}{10} = \boxed{150}</math> oranges.
  
 
==See Also==
 
==See Also==

Latest revision as of 03:01, 14 June 2022

A boy buys oranges at $3$ for $10$ cents. He will sell them at $5$ for $20$ cents. In order to make a profit of $$1.00$, he must sell:

$\textbf{(A)}\ 67 \text{ oranges} \qquad \textbf{(B)}\ 150 \text{ oranges} \qquad \textbf{(C)}\ 200\text{ oranges}\\  \textbf{(D)}\ \text{an infinite number of oranges}\qquad \textbf{(E)}\ \text{none of these}$

Solution

The boy buys $3$ oranges for $10$ cents or $1$ orange for $\frac{10}{3}$ cents. He sells them at $\frac{20}{5}=4$ cents each. That means for every orange he sells, he makes a profit of $4-\frac{10}{3}=\frac{2}{3}$ cents.

To make a profit of $100$ cents, he needs to sell $\frac{100}{\frac{2}{3}}=\boxed{150}=\boxed{\text{B}}$

~mathsolver101

Solution 2

The boy buys $3$ oranges for $10$ cents. He sells them at $5$ for $20$ cents. So, he buys $15$ for $50$ cents and sells them at $15$ for $60$ cents, so he makes $10$ cents of profit on every $15$ oranges. To make $100$ cents of profit, he needs to sell $15 \cdot \frac{100}{10} = \boxed{150}$ oranges.

See Also

1953 AHSC (ProblemsAnswer KeyResources)
Preceded by
First Question
Followed by
Problem 2
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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

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