Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 7"
(→Solution) |
m (→Solution) |
||
(4 intermediate revisions by one other user not shown) | |||
Line 2: | Line 2: | ||
Each card below covers up a number. The number written below each card is the sum of all the numbers covered by all of the other cards. What is the sum of all of the hidden numbers? | Each card below covers up a number. The number written below each card is the sum of all the numbers covered by all of the other cards. What is the sum of all of the hidden numbers? | ||
− | + | <center>[[Image:Usc93.7.PNG]]</center> | |
<center><math> \mathrm{(A) \ }4.2 \qquad \mathrm{(B) \ }5 \qquad \mathrm{(C) \ }5.6 \qquad \mathrm{(D) \ }6.2 \qquad \mathrm{(E) \ }6.8 </math></center> | <center><math> \mathrm{(A) \ }4.2 \qquad \mathrm{(B) \ }5 \qquad \mathrm{(C) \ }5.6 \qquad \mathrm{(D) \ }6.2 \qquad \mathrm{(E) \ }6.8 </math></center> | ||
Line 8: | Line 8: | ||
== Solution == | == Solution == | ||
If we call the squares <math>a,b,c,d,e,f</math> (in order from left to right), we have: | If we call the squares <math>a,b,c,d,e,f</math> (in order from left to right), we have: | ||
− | <math>b+c+d+e+f=3</math> | + | <math>b+c+d+e+f=3</math>, |
− | <math>a+c+d+e+f=8</math> | + | <math>a+c+d+e+f=8</math>, |
− | <math>a+b+d+e+f=5</math> | + | <math>a+b+d+e+f=5</math>, |
− | <math>a+b+c+e+f=6</math> | + | <math>a+b+c+e+f=6</math>, |
− | <math>a+b+c+d+f=2</math> | + | <math>a+b+c+d+f=2</math>, |
− | <math>a+b+c+d+e=4</math> | + | <math>a+b+c+d+e=4</math>. |
− | Adding all the equations gives us <math> 5(a + b + c + d + e)=28 \Longrightarrow a + b + c + d + e = 5.6</math>. | + | Adding all the equations gives us <math>5 (a + b + c + d + e) = 28 \Longrightarrow a + b + c + d + e = 5.6 </math>. |
− | + | ---- | |
− | * [[University of South Carolina High School Math Contest/1993 Exam]] | + | |
+ | * [[University of South Carolina High School Math Contest/1993 Exam/Problem 6|Previous Problem]] | ||
+ | * [[University of South Carolina High School Math Contest/1993 Exam/Problem 8|Next Problem]] | ||
+ | * [[University of South Carolina High School Math Contest/1993 Exam|Back to Exam]] | ||
+ | |||
+ | [[Category:Introductory Algebra Problems]] |
Latest revision as of 13:09, 12 October 2007
Problem
Each card below covers up a number. The number written below each card is the sum of all the numbers covered by all of the other cards. What is the sum of all of the hidden numbers?
![$\mathrm{(A) \ }4.2 \qquad \mathrm{(B) \ }5 \qquad \mathrm{(C) \ }5.6 \qquad \mathrm{(D) \ }6.2 \qquad \mathrm{(E) \ }6.8$](http://latex.artofproblemsolving.com/b/9/e/b9ea45696aca89b031c2973ecfc5f973ace67524.png)
Solution
If we call the squares (in order from left to right), we have:
,
,
,
,
,
.
Adding all the equations gives us
.