Difference between revisions of "1985 AJHSME Problems/Problem 6"
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<math>\text{(A)}\ 250 \qquad \text{(B)}\ 550 \qquad \text{(C)}\ 667 \qquad \text{(D)}\ 750 \qquad \text{(E)}\ 1250</math> | <math>\text{(A)}\ 250 \qquad \text{(B)}\ 550 \qquad \text{(C)}\ 667 \qquad \text{(D)}\ 750 \qquad \text{(E)}\ 1250</math> | ||
| − | ==Solution== | + | ==Solution 1== |
| − | |||
We could solve the first equation for the thickness of one sheet of paper, and divide into the 2nd equation (which is one way to do the problem), but there are other ways, too. | We could solve the first equation for the thickness of one sheet of paper, and divide into the 2nd equation (which is one way to do the problem), but there are other ways, too. | ||
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<math>750</math> is <math>\boxed{\text{D}}</math> | <math>750</math> is <math>\boxed{\text{D}}</math> | ||
| + | |||
| + | ==Solution 2== | ||
| + | We can set up a direct proportion relating the amount of sheets to the thickness because according to the problem, all the papers have the same thickness. | ||
| + | Our proportion is <cmath>\frac{5}{500}=\frac{7.5}{x}</cmath> where <math>x</math> is the number we are looking for. | ||
| + | Next, we cross-multiply to get <math>5x=500 \times 7.5</math> so <math>x=750</math> which is <math>\boxed{\text{D}}</math> | ||
| + | |||
| + | ~GrantStar | ||
| + | |||
| + | ==Solution 3 (Very quick, use this to do the problem quickly)== | ||
| + | We immediately see <math>500</math> sheets of paper per <math>5</math>cm is <math>\frac{500}{5}</math>, which can be simplified to <math>\frac{100}{1}</math>. The denominator is supposed to be <math>7.5</math>. We can now just multiply the numerator, <math>100</math>, by <math>7.5</math>, to get <math>\boxed{\textbf{(D)}\ 750}</math>. | ||
| + | ~[[shunyipanda]] | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/Dp1i5sCWN_c | ||
| + | |||
| + | ~savannahsolver | ||
==See Also== | ==See Also== | ||
Latest revision as of 18:13, 23 October 2025
Contents
Problem
A ream of paper containing 
sheets is 
cm thick. Approximately how many sheets of this type of paper would there be in a stack 
cm high?
Solution 1
We could solve the first equation for the thickness of one sheet of paper, and divide into the 2nd equation (which is one way to do the problem), but there are other ways, too.
Let's say that 
. So by multiplying 
by this fraction, we SHOULD get the number of sheets in 7.5 cm. Solving gets
is 
Solution 2
We can set up a direct proportion relating the amount of sheets to the thickness because according to the problem, all the papers have the same thickness.
Our proportion is ![\[\frac{5}{500}=\frac{7.5}{x}\]](http://latex.artofproblemsolving.com/3/2/2/322ffa4ac9e88e8a80217fc7e5f072608e6bbe6b.png)
where 
is the number we are looking for.
Next, we cross-multiply to get 
so 
which is
~GrantStar
Solution 3 (Very quick, use this to do the problem quickly)
We immediately see sheets of paper per cm is 
, which can be simplified to 
. The denominator is supposed to be . We can now just multiply the numerator, 
, by , to get 
.
~shunyipanda
Video Solution
~savannahsolver
See Also
| 1985 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
