SOLUTION: There are 538 electoral votes. The value of x is 110 more than y. The value of y is 145 more than z. Write an equation involving the variables x, y, and z, that represents the tota

Question 263056: There are 538 electoral votes. The value of x is 110 more than y. The value of y is 145 more than z. Write an equation involving the variables x, y, and z, that represents the total number of electoral votes.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
You are asked to partition 538 into components x, y, and z.
x + y + z = 538
.
That is perhaps the answer to your question, but given the other statements in the problem setup, it seems that you would need to find the values of x, y, and z.
.
The problem states:
x = y +110 or y = x -110
.
y = z + 145 or z = y -145
.
Substituting:
(y+110) + y + (y-145) = 538
Collecting like terms:
3y -35 = 538
Adding 35 to both sides:
3y = 573
Dividing both sides by 3:
y = 191
.
Substituting into our original equations:
x = y + 110 = 191+110= 301
z = y - 145 = 191-145 = 46
.
Checking we have:
301 + 191 + 46 = 538?
Yes it does.
.
So we can say:
x = 301
y = 191
z = 46
.
Done.
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