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Difference between revisions of "1987 AJHSME Problems/Problem 15"

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<math>\text{(A)}\ 59.25\text{ dollars} \qquad \text{(B)}\ 60\text{ dollars} \qquad \text{(C)}\ 70\text{ dollars} \qquad \text{(D)}\ 79\text{ dollars} \qquad \text{(E)}\ 80\text{ dollars}</math>
 
<math>\text{(A)}\ 59.25\text{ dollars} \qquad \text{(B)}\ 60\text{ dollars} \qquad \text{(C)}\ 70\text{ dollars} \qquad \text{(D)}\ 79\text{ dollars} \qquad \text{(E)}\ 80\text{ dollars}</math>
  
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==Solution==
+
==Solution 1==
  
 
Let the regular price of one tire be <math>x</math>.  We have  
 
Let the regular price of one tire be <math>x</math>.  We have  
Line 15: Line 15:
 
<math>\boxed{\text{D}}</math>
 
<math>\boxed{\text{D}}</math>
 
Good Job!
 
Good Job!
 +
==Solution 2==
 +
To get the price, we can also work backwards without introducing a variable.
  
 +
To get the price of all of the tires outside of the fourth tire, we can subtract <math>3</math> from the total, which gives <math>240 - 3</math> = <math>237</math>.
 +
 +
Dividing this by <math>3</math> to get the price of a single tire without the sale, we get:
 +
 +
<math>\frac{237}{3} = \boxed {\textbf {(D) } 79}</math>
 
==See Also==
 
==See Also==
  

Revision as of 13:01, 18 June 2025

Problem

The sale ad read: "Buy three tires at the regular price and get the fourth tire for 3 dollars." Sam paid 240 dollars for a set of four tires at the sale. What was the regular price of one tire?

$\text{(A)}\ 59.25\text{ dollars} \qquad \text{(B)}\ 60\text{ dollars} \qquad \text{(C)}\ 70\text{ dollars} \qquad \text{(D)}\ 79\text{ dollars} \qquad \text{(E)}\ 80\text{ dollars}$

Solution 1

Let the regular price of one tire be $x$. We have \begin{align*} 3x+3=240 &\Rightarrow 3x=237 \\ &\Rightarrow x=79 \end{align*}

$\boxed{\text{D}}$ Good Job!

Solution 2

To get the price, we can also work backwards without introducing a variable.

To get the price of all of the tires outside of the fourth tire, we can subtract $3$ from the total, which gives $240 - 3$ = $237$.

Dividing this by $3$ to get the price of a single tire without the sale, we get:

$\frac{237}{3} = \boxed {\textbf {(D) } 79}$

See Also

1987 AJHSME (Problems • Answer Key • Resources)
Preceded by
Problem 14 		Followed by
Problem 16
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 AJHSME/AMC 8 Problems and Solutions

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