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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