Difference between revisions of "2007 AMC 8 Problems/Problem 5"
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== Problem == | == Problem == | ||
| − | Chandler wants to buy a <math> | + | Chandler wants to buy a <math>$</math>500<math> mountain bike. For his birthday, his grandparents |
| − | send him | + | send him </math>$<math>50</math>, his aunt sends him <math>$</math>35<math> and his cousin gives him </math>$<math>15</math>. He earns |
| − | <math> | + | <math>$</math>16<math> per week for his paper route. He will use all of his birthday money and all |
of the money he earns from his paper route. In how many weeks will he be able | of the money he earns from his paper route. In how many weeks will he be able | ||
to buy the mountain bike? | to buy the mountain bike? | ||
| − | <math>\mathrm{(A)}\ 24 \qquad\mathrm{(B)}\ 25 \qquad\mathrm{(C)}\ 26 \qquad\mathrm{(D)}\ 27 \qquad\mathrm{(E)}\ 28< | + | </math>\mathrm{(A)}\ 24 \qquad\mathrm{(B)}\ 25 \qquad\mathrm{(C)}\ 26 \qquad\mathrm{(D)}\ 27 \qquad\mathrm{(E)}\ 28<math> |
== Solution == | == Solution == | ||
| − | Let <math>x< | + | Let </math>x<math> be the number of weeks. |
| − | Thus, we have the equation <math>50 + 35 + 15 + 16x = 500< | + | Thus, we have the equation </math>50 + 35 + 15 + 16x = 500<math>. |
Simplify, | Simplify, | ||
| − | <math>100 + 16x = 500< | + | </math>100 + 16x = 500<math> |
| − | <math>16x = 400< | + | </math>16x = 400<math> |
| − | <math>x = 25< | + | </math>x = 25<math> |
| − | The answer is <math> \boxed{\textbf{(B)}\ 25} | + | The answer is </math> \boxed{\textbf{(B)}\ 25} $ |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2007|num-b=4|num-a=6}} | {{AMC8 box|year=2007|num-b=4|num-a=6}} | ||
| + | {{MAA Notice}} | ||
Revision as of 00:23, 5 July 2013
Problem
Chandler wants to buy a 
500
$
, his aunt sends him 35
$
. He earns
16
\mathrm{(A)}\ 24 \qquad\mathrm{(B)}\ 25 \qquad\mathrm{(C)}\ 26 \qquad\mathrm{(D)}\ 27 \qquad\mathrm{(E)}\ 28$== Solution ==
Let$ (Error compiling LaTeX. Unknown error_msg)x$be the number of weeks.
Thus, we have the equation$ (Error compiling LaTeX. Unknown error_msg)50 + 35 + 15 + 16x = 500$.
Simplify,$ (Error compiling LaTeX. Unknown error_msg)100 + 16x = 500$$ (Error compiling LaTeX. Unknown error_msg)16x = 400$$ (Error compiling LaTeX. Unknown error_msg)x = 25
\boxed{\textbf{(B)}\ 25} $
See Also
| 2007 AMC 8 (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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
