SOLUTION: The sum of two integers is 85. Ten less than three times the smaller of the integers is equal to twenty more than twice the larger integer. Find the numbers using only one unknown.

Question 737226: The sum of two integers is 85. Ten less than three times the smaller of the integers is equal to twenty more than twice the larger integer. Find the numbers using only one unknown.
I tried doing it using two unknowns and i got 41 and 47.
Found 2 solutions by rothauserc, lwsshak3:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we know that i+j = 85 and
3i-10 = 2j+20
solve for i = 2j/3 + 10/3
substitute in equation 1 for i
2j/3 +10/3 + j = 85
multiply both sides by 3
2j + 10 + 3j = 255
5j = 245 and j = 49 and i = 36

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The sum of two integers is 85. Ten less than three times the smaller of the integers is equal to twenty more than twice the larger integer. Find the numbers using only one unknown.
***
let x=smaller of two integers
85-x=larger of two integers
...
Ten less than three times the smaller of the integers=3x-10
twenty more than twice the larger integer=2(85-x)+20
..
3x-10=2(85-x)+20
3x-10=170-2x+20
5x=200
x=40
85-x=45
smaller of two integers=40
larger of two integers=45
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