SOLUTION: the sum of two is 16. five times of the smaller number exceeds the larger number by 68. find the number

Question 636467: the sum of two is 16. five times of the smaller number exceeds the larger number by 68. find the number
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let S = the smaller number
and L = the larger number
The first statement is
S + L = 16 (1)
The second is
5*S = L + 68 (2)
Solve (2) for L yields
L = 5*S - 68 (3)
Substitute L of (3) into (1) yields
S + 5*S - 68 = 16 (4)
Simplify (4) to obtain
6*S = 84 or
S = 84/6
S = 14 (5)
Substitute 14 for S in (3) yields
L = 5*14 -68
L = 70 - 68
L = 2
Let's check this reult using (1)
Is (S+L=16)?
Is (14+2=16)?
Is (16=16)? Yes
Our answer is that the smaller number is 14 and the larger number is 2. This is contrary to the definition of the two numbers. The second statement should be reversed to state that "five time of the larger number exceeds the smaller number by 68." Then the answer is "the smaller number is 2 and the larger 14."

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