Sum of three students grades

Question

Question:

 

"The sum of three students math grade is 249. Gina's grade is 52 points less than Jessica's grade. Haley's grade is 49 more than one-half Jessica's grade. Write and solve an algebaic equation to find the grades for each student.

Answer 1

Let G for Gina’s grade
J for Jessica's
H for Haley's
Given G + J + H =249 ...........(1)
G = J -52....................................(2)
H = J/2 +49 ........................(3)
Substituting values of (2) in (1)
G +G+52 +H =249 or
2G +H = 197.................................(4)
From (2) and (3)
2H –G = 150..................................(5)
Solving (4) and (5)
H= 497/5 = 99.4
And G = 48.8
Substituting the values of H and G in (1)
48.8 +J + 99.4 = 249
J = 100.8

Answer 2

Sum of the 3 grades is 249:

G + J + H = 249 __________ eqn 1

 

Gina's grade is 52 less than Jessica's

G = J - 52  _____________ eqn 2

 

Haley got 49 more than half of Jessica's grade
H = J/2 + 49 _________ eqn 3

 

Use substitution:  In equation 1 replace

G with J-52 and replace H with J/2 + 49

 

J-52 + J + J/2 + 49 = 249

 

(2 1/2)J -3 = 249

 

(5/2)J = 252

 

J = 252(2/5)

 

J = 100.8

 

Jessica got a score of 100.8   (extra bonus question maybe?)

 

From there:

G = J - 52

 

H = J/2 + 49