Difference between revisions of "1995 AJHSME Problems/Problem 5"
Talkinaway (talk | contribs) (Created page with "==Problem== Find the smallest whole number that is larger than the sum <cmath>2\dfrac{1}{2}+3\dfrac{1}{3}+4\dfrac{1}{4}+5\dfrac{1}{5}.</cmath> <math>\text{(A)}\ 14 \qquad \tex...") |
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<math>\text{(A)}\ 14 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 16 \qquad \text{(D)}\ 17 \qquad \text{(E)}\ 18</math> | <math>\text{(A)}\ 14 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 16 \qquad \text{(D)}\ 17 \qquad \text{(E)}\ 18</math> | ||
| − | ==Solution 1== | + | ==Solution== |
| + | ===Solution 1=== | ||
Adding the whole numbers gives <math>2 + 3 + 4 + 5 = 14</math>. | Adding the whole numbers gives <math>2 + 3 + 4 + 5 = 14</math>. | ||
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Adding the fractions gives <math>\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} = \frac{30}{60} + \frac{20}{60} + \frac{15}{60} + \frac{12}{60} = \frac{77}{60}</math>. This will create one more whole, and a fraction that is less than <math>1</math>. Thus, the smalleset whole number that is less than <math>15</math> plus some fractional part is <math>16</math>, and the answer is <math>\boxed{C}</math>. | Adding the fractions gives <math>\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} = \frac{30}{60} + \frac{20}{60} + \frac{15}{60} + \frac{12}{60} = \frac{77}{60}</math>. This will create one more whole, and a fraction that is less than <math>1</math>. Thus, the smalleset whole number that is less than <math>15</math> plus some fractional part is <math>16</math>, and the answer is <math>\boxed{C}</math>. | ||
| − | ==Solution 2== | + | ===Solution 2=== |
Convert the fractional parts to decimals, and approximate the answer. <math>2.5 + 3.33 + 4.25 + 5.2 = 15.28</math>, and the answer is <math>16</math>, which is <math>\boxed{C}</math>. | Convert the fractional parts to decimals, and approximate the answer. <math>2.5 + 3.33 + 4.25 + 5.2 = 15.28</math>, and the answer is <math>16</math>, which is <math>\boxed{C}</math>. | ||
Revision as of 02:57, 23 December 2012
Problem
Find the smallest whole number that is larger than the sum
![\[2\dfrac{1}{2}+3\dfrac{1}{3}+4\dfrac{1}{4}+5\dfrac{1}{5}.\]](http://latex.artofproblemsolving.com/3/5/9/35976a4939b2325cb240645d8b440c560c990701.png)
Solution
Solution 1
Adding the whole numbers gives 
.
Adding the fractions gives 
. This will create one more whole, and a fraction that is less than 
. Thus, the smalleset whole number that is less than 
plus some fractional part is 
, and the answer is 
.
Solution 2
Convert the fractional parts to decimals, and approximate the answer. 
, and the answer is , which is .
See Also
| 1995 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 | ||
