Difference between revisions of "1987 AJHSME Problems/Problem 10"

(New page: ==Problem== <math>4(299)+3(299)+2(299)+298=</math> <math>\text{(A)}\ 2889 \qquad \text{(B)}\ 2989 \qquad \text{(C)}\ 2991 \qquad \text{(D)}\ 2999 \qquad \text{(E)}\ 3009</math> ==Soluti...)
 
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==See Also==
 
==See Also==
  
[[1987 AJHSME Problems]]
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{{AJHSME box|year=1987|num-b=9|num-a=11}}
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[[Category:Introductory Algebra Problems]]

Revision as of 20:21, 27 May 2009

Problem

$4(299)+3(299)+2(299)+298=$

$\text{(A)}\ 2889 \qquad \text{(B)}\ 2989 \qquad \text{(C)}\ 2991 \qquad \text{(D)}\ 2999 \qquad \text{(E)}\ 3009$

Solution

We can make use of the distributive property as follows: \begin{align*} 4(299)+3(299)+2(299)+298 &= 4(299)+3(299)+2(299)+1(299)-1 \\ &= (4+3+2+1)(299)-1 \\ &= 10(299)-1 \\ &= 2989 \\ \end{align*}

$\boxed{\text{B}}$

See Also

1987 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
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