SOLUTION: Good evening. I have the following word problem and I was wondering if I can find some help. Thanks in advance. "The total of Dharma's, Eugenio's, and Fern's final exam scores

Algebra.Com
Question 1175237: Good evening. I have the following word problem and I was wondering if I can find some help. Thanks in advance.
"The total of Dharma's, Eugenio's, and Fern's final exam scores is 271. If Dharma's score is added to Eugenio's score, the sum is 11 points less than twice Fern's score. If Eugenio's score is 5 points higher than Dharma's score, what is each student's final exam score?"
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi
Eugenio's score is 5 points higher than Dharma's "x"
x + (x+5) = 2F - 11
(2x +16)/2 = F = x+8
x + (x+5) + (x+8) = 271
           3x = 258
            x = 86 is Dharma's score.
 Eugenio's score is 91  and Fern's score is 94
 86 + 91 + 94 = 271 checks
Wish You the Best in your Studies.


Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Let x be the Dharma' scores.


Then Eugenio' scores is  (x+5), according to the condition.


Dharma' scores plus Eugenio' scores is  x + (x+5) = 2x + 5.


This sum is 11 points less than twice Fern' scores --- so, 

twice Fern' scores is  ((2x+5)+11) = 2x+16.

Hence,  Fern' scores is  (2x+16)/2 = x+8.



The total of the scores is 271, giving you equation for x

    x + (x+5) + (x+8) = 271


Simplify and solve


    3x + 13 = 271

    3x      = 271 - 13 = 258

     x                 = 258/3 = 86.


Hence, Dharma has  86 points;  Eugenio has  86+5 = 91 points;  Fern has x+8 = 86+8 = 94 points.    ANSWER

Solved.


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