The total of dharma's, Eugene, and Ferns final exam score is 272 Dharma score is added to Eugene score the sum is 28 points less than twice ferns score if Eugene score is eight point higher than Dharma score what is each student's final an exam score?
X = Ferns' score.
2x-28 = D. + E. score.
x + 2x-28 = 272.
3x = 300.
X = 100.
2x-28 = 2*100 - 28 = 172 = D. + E.
Y = D. score.
Y+8 = E. score.
Y + Y+8 = 172.
2y = 164.
Y = 82.
Y+8 = 82 + 8 = 90.
To solve this problem, let's assign variables to each student's score.
Let:
D = Dharma's score
E = Eugene's score
F = Fern's score
We are given that the total of Dharma's, Eugene's, and Fern's final exam score is 272:
D + E + F = 272 ----(1)
We are also given that when Dharma's score is added to Eugene's score, the sum is 28 points less than twice Fern's score:
D + E = 2F - 28 ----(2)
Lastly, we know that Eugene's score is 8 points higher than Dharma's score:
E = D + 8 ----(3)
We can now solve the system of equations formed by equations (1), (2), and (3).
Substituting equation (3) into equation (2), we get:
(D + 8) + E = 2F - 28
D + E + 8 = 2F - 28
Substituting equations (3) and (2) into equation (1), we get:
(D + 8) + D + F = 272
2D + 8 + F = 272
2D + F = 264
Now we have a system of two equations with two variables:
2D + F = 264 ----(4)
D + E + 8 = 2F - 28 ----(5)
We can solve this system of equations to find the values of D, E, and F.