SOLUTION: Please help me solve this equation: Number solving Using three equations: Kristen has a total of 225 on three tests. The sum of the scores on the first and second tests exce

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Question 168846This question is from textbook Prentice Hall algebra2 with trigonometry
: Please help me solve this equation:
Number solving Using three equations:
Kristen has a total of 225 on three tests. The sum of the scores on the first and second tests exceeds her third score by 61. her first score exceeds her second by 6. Find the 3 scores. This question is from textbook Prentice Hall algebra2 with trigonometry

Found 2 solutions by scott8148, Mathtut:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
letx="1st test", y="2nd test", and z="3rd test"

"Kristen has a total of 225 on three tests" __ x+y+z=225

" The sum of the scores on the first and second tests exceeds her third score by 61" __ x+y=z+61

"her first score exceeds her second by 6" __ x=y+6

substituting from 2nd equation into 1st __ (z+61)+z=225 __ 2z+61=225 __ 2z=164 __ z=82

substituting from 3rd eqn into 2nd __ (y+6)+y=(82)+61 __ 2y+6=143 __ 2y=137 __ y=68.5

substituting into 3rd eqn __ x=(68.5)+6 __ x=74.5

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the scores on her 3 tests a,b,and c
a+b+c=225...eq 1
a+b=c+61....eq 2
a=b+6.......eq 3
lets plug a's value from eq 3 into b+6+b=c+61----solve for c in terms of b
c=2b-55.
now we take this value of c and a's value from eq 3 and plug them into eq 1
:
(b+6)+b+2b-55=225
4b=164
:
highlight%28b=68.5%29score
highlight%28a=68.5%2B6=74.5%29score
highlight%28c=2%2868.5%29-55=82%29score