Difference between revisions of "2000 AMC 8 Problems/Problem 1"
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Aunt Anna is <math>42</math> years old. Caitlin is <math>5</math> years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin? | Aunt Anna is <math>42</math> years old. Caitlin is <math>5</math> years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin? | ||
| − | <math> | + | <math>\mathrm{(A)}\ 15\qquad\mathrm{(B)}\ 16\qquad\mathrm{(C)}\ 17\qquad\mathrm{(D)}\ 21\qquad\mathrm{(E)}\ 37</math> |
| − | \mathrm{(A)}\ 15 | + | |
| − | \qquad | + | ==Solution== |
| − | \mathrm{(B)}\ 16 | + | ===Solution 1=== |
| − | \qquad | ||
| − | \mathrm{(C)}\ 17 | ||
| − | \qquad | ||
| − | \mathrm{(D)}\ 21 | ||
| − | \qquad | ||
| − | \mathrm{(E)}\ 37 | ||
| − | </math> | ||
| − | == Solution == | ||
If Brianna is half as old as Aunt Anna, then Briana is <math>\frac{42}{2}</math> years old, or <math>21</math> years old. | If Brianna is half as old as Aunt Anna, then Briana is <math>\frac{42}{2}</math> years old, or <math>21</math> years old. | ||
| Line 19: | Line 11: | ||
So, the answer is <math>\boxed{B}</math> | So, the answer is <math>\boxed{B}</math> | ||
| − | ==Solution== | + | |
| + | ===Solution 2=== | ||
Since Brianna is half of Aunt Anna's age this means that Brianna is <math>21</math> years old. | Since Brianna is half of Aunt Anna's age this means that Brianna is <math>21</math> years old. | ||
Now we just find Caitlin's age by doing <math>21-5</math>. This makes <math>16</math> or <math>\boxed{B}</math> | Now we just find Caitlin's age by doing <math>21-5</math>. This makes <math>16</math> or <math>\boxed{B}</math> | ||
==See Also== | ==See Also== | ||
| − | |||
{{AMC8 box|year=2000|before=First<br />Question|num-a=2}} | {{AMC8 box|year=2000|before=First<br />Question|num-a=2}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 21:17, 11 February 2020
Problem
Aunt Anna is 
years old. Caitlin is 
years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?
Solution
Solution 1
If Brianna is half as old as Aunt Anna, then Briana is 
years old, or 
years old.
If Caitlin is years younger than Briana, she is 
years old, or 
.
So, the answer is 
Solution 2
Since Brianna is half of Aunt Anna's age this means that Brianna is years old.
Now we just find Caitlin's age by doing . This makes or
See Also
| 2000 AMC 8 (Problems • Answer Key • Resources) | ||
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
