Answer :
Answers: 4 and 7
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Work Shown
p = smaller number
q = larger number
3p = q+5 since "three times the smaller number exceeds the larger by 5".
That solves to q = 3p-5 which will be useful in the substitution step shown below.
We're told "the sum of the numbers is 11", so,
p+q = 11
p+3p-5 = 11 ...... substitution; replace q with 3p-5
4p-5 = 11
4p = 11+5
4p = 16
p = 16/4
p = 4 is the smaller number.
q = 3p-5 = 3*4-5 = 12-5 = 7 is the larger number.
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Check:
- The condition 3*smaller = larger + 5 is met since 3*4 = 7+5 is true.
- smaller + larger = 4+7 = 11 showing the two items sum to 11.
Both conditions have been verified.
