SOLUTION: The sum of a student's three scores is 212. If the first is 20 points more than the second, and the sum of the first two is 32 more than twice the third, what was the first score?

Question 632799: The sum of a student's three scores is 212. If the first is 20 points more than the second, and the sum of the first two is 32 more than twice the third, what was the first score?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Three scores, a, b, c
Write an equation for each statement:
:
The sum of a student's three scores is 212.
a + b + c = 212
:
If the first is 20 points more than the second,
a = b+20
a - b = 20
:
and the sum of the first two is 32 more than twice the third,
a + b = 2c + 32
a + b - 2c = 32
Subtract from the 1st equation
a + b + c = 212
a + b -2c = 32
----------------subtraction eliminates a and b
3c = 180
c = 180/3
c = 60 the 3rd score
:
Find a
a + b + 60 = 212
subtract 60 from both sides
a + b = 152
Add a - b = 20 to the above equation
a + b = 152
a - b = 20
-------------addition eliminates b, find a
2a = 172
a = 172/2
a = 86 is the 1st score
:
:
To confirm this find b
86 - b = 20
b = 66
:
Total of all three scores
86 + 66 + 60 = 212

:

RELATED QUESTIONS
The sum of a student's three scores is 217. If the first is 16 points more than the... (answered by ewatrrr)

The sum of a student's three scores is 228. If the first is 21 points more than the... (answered by ankor@dixie-net.com)

the sum of a students three scores is 220. if the first is 23 points more than the... (answered by fractalier)

The sum of a student's three scores is 210. If the first is 23 points more than the... (answered by josgarithmetic,MathTherapy)

The sum of a student's three scores is 228. If the first is 21 points more than the... (answered by ikleyn)

A student has a total of 244 points from 3 tests. The first test score was 20 more than... (answered by checkley75,mathemanic)

What is the sum of three consecutive odd integers if the sum of the second and third... (answered by SAT Math Tutor)

what is the sum of three consecutive odd integers if the sum of the second and third... (answered by Earlsdon)

What is the sum of three consecutive odd integers if the sum of the second and third... (answered by algebrahouse.com)