SOLUTION: The total of two integers is forty three. Double the larger integer exceeds 3 times the smaller integer by sixteen. What are the integers?

Question 1019837: The total of two integers is forty three. Double the larger integer exceeds 3 times the smaller integer by sixteen. What are the integers?
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Let I = the first integer
Let J = the second integer
I + J = 43
2J = 3I + 16
Rework I + J = 43 by adding -I to each side
J = 43 - I
Now substitute (43 - I) for J in 2J = 3I + 16
2(43 - I) = 3I + 16
86 - 2I = 3I + 16
add 2I to each side
86 = 5I + 16
add -16 to each side
70 = 5I
14 = I
Since J = 43 - I, substitute 14 for I
J = 43 - 14
J = 29
Checking our original equations
I + J = 43 , 14 + 29 = 43 so this checks out
2J = 3I + 16 , 2(29) = 3(14) + 16 , 58 = 42 + 16 , so this checks out
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