SOLUTION: The sum of two numbers is 103. If four times the smaller number is subtracted from the larger number, the result is 8. Find the two numbers.

Question 924988: The sum of two numbers is 103. If four times the smaller number is subtracted from the larger number, the result is 8. Find the two numbers.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let L = the larger number and
Let s = the smaller number
From the problem statement we have
(1) s + L = 103 and
(2) L - 4*s = 8
You need, and have, two equations to solve for two unknowns (the two numbers).
You can use any of the techniques you learned to solve simultaneous equations. Let's use substitution. Solve (2) for L and get
(3) L = 8 + 4*s
Now put L of (3) into (1) and get
(4) s + 8 + 4*s = 103 or
(5) 5*s = 103 - 8 or
(6) 5*s = 95 or
(7) s = 95/5 or
(8) s = 19
Now put s of (8) into (2) to get
(9) L - 4*19 = 8 or
(10) L = 8 + 4*19 or
(11) L = 8 + 76 or
(12) L = 84
Now use (2) to check your answer.
Is (L - 4*S = 8)?
Is (84 - 4*19 = 8)?
Is (84 -76 = 8)?
Is (8 = 8)? Yes
Answer: The smaller number is 19 and the larger number is 84.
REM: you need to write two independent equations to solve for two unknowns. If you have three unknowns, like in many coin problems, you need three independent equations, etc. etc.

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