Difference between revisions of "1985 AJHSME Problems/Problem 18"

Revision as of 16:39, 27 March 2015

Problem

Nine copies of a certain pamphlet cost less than <dollar/> $10.00$ while ten copies of the same pamphlet (at the same price) cost more than <dollar/> $11.00$ . How much does one copy of this pamphlet cost?

$\text{(A)}$ $$1.07$

$\text{(B)}$ $$1.08$

$\text{(C)}$ $$1.09$

$\text{(D)}$ $$1.10$

$\text{(E)}$ $$1.11$

Solution

Let $p$ be the cost of the first pamphlet, in dollars. The first part tells us $9p<10 \Rightarrow p<1.\overline{1}$

The second part tells us that $10p>11\Rightarrow p>1.1$

Combining these two parts, the only possible value for $p$ is $1.11$ , since $p$ represents a monetary value.

$\boxed{\text{E}}$

1985 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 3: / Line 3: @@
 Nine copies of a certain pamphlet cost less than <dollar/><math>10.00</math> while ten copies of the same pamphlet (at the same price) cost more than <dollar/><math>11.00</math>.  How much does one copy of this pamphlet cost?
-<math>\text{(A)}</math> <dollar/><math>1.07</math>
+<math>\text{(A)}</math> <math>\$1.07</math>
-<math>\text{(B)}</math> <dollar/><math>1.08</math>
+<math>\text{(B)}</math> <math>\$1.08</math>
-<math>\text{(C)}</math> <dollar/><math>1.09</math>
+<math>\text{(C)}</math> <math>\$1.09</math>
-<math>\text{(D)}</math> <dollar/><math>1.10</math>
+<math>\text{(D)}</math> <math>\$1.10</math>
-<math>\text{(E)}</math> <dollar/><math>1.11</math>
+<math>\text{(E)}</math> <math>\$1.11</math>
 ==Solution==

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Difference between revisions of "1985 AJHSME Problems/Problem 18"

Revision as of 16:39, 27 March 2015

Problem

Solution

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