SOLUTION: The sum of two numbers is 20. The difference between their product and their sum yields 71. Find the smaller number

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Question 963804: The sum of two numbers is 20. The difference between their product and their sum yields 71. Find the smaller number
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
S=smaller number;L=larger number
S%2BL=20
L=20-S
%28S%29%28L%29-20=71
%28S%29%28L%29=91 Substitute for L
%28S%29%2820-S%29=91
-S%5E2%2B20S=91
-S%5E2%2B20S-91=0
S%5E2-20S%2B91=0
%28S-13%29%28S-7%29=0
S-13=0 or S-7=0
S=13 or S=7
ANSWER: The smaller number is 7.
CHECK:
%28%28S%29%28L%29%29-%28S%2BL%29=71
%28%287%29%2813%29%29-%287%2B13%29=71
91-20=71
71=71