SOLUTION: This problem is absolutely stumping me...any help would be appreciated. "A student scored a total of 258 points on three tests. The total of her first two scores was 80 points m

Click here to see ALL problems on Linear-systems

Question 1032024: This problem is absolutely stumping me...any help would be appreciated.
"A student scored a total of 258 points on three tests. The total of her first two scores was 80 points more than her third score. She scored 13 points more on her third test than on her second. What were her scores on all three tests?"
Thank you
Found 2 solutions by fractalier, stanbon:
Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website!
Let's call her scores on the tests, x, y and z.
Then we write
x + y + z = 258
We also have
x + y = z + 80
and
z = y + 13
We can plug in the second into the first equation and get
z + 80 + z = 258
2z + 80 = 258
2z = 178
z = 89
so that
y = 76
and now
x + 76 + 89 = 258
we can find that
x = 258 - 76 - 89 = 93
Her scores were then
93, 76 and 89.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
student scored a total of 258 points on three tests. The total of her first two scores was 80 points more than her third score. She scored 13 points more on her third test than on her second. What were her scores on all three tests?"
------
Equations:
f + s + t = 258 points
f+s = t+80
t = s + 13
-----------------------
Substitute to get one variable::
t = s+13
f = t-s+80 = (s+13)-s + 80 = 93 (first test score)
-------
So::
93 + s + s+13 = 258
2s + 106 = 258
2s = 152
s = 76 points (second test score)
t = s+ 13 = 89 (third test score)
--------------------------
Cheers,
Stan H.
------------