Question 1205571
<br>
Although the re-wording of the problem as suggested by the other tutor would make the problem easier to read, there is in fact no ambiguity in the given wording.<br>
"A is less than B by 11" means exactly the same thing as "A is 11 less than B".<br>
To solve the problem as stated....<br>
Let x be the units digit
Then x+4 is the tens digit<br>
The 2-digit number is then {{{10(x+4)+x=11x+40}}}<br>
The product of the digits is {{{x(x+4)=x^2+4x}}}<br>
The two-digit number is less than 4 times the product of its digits by 11:<br>
{{{11x+40=4(x^2+4x)-11}}}
{{{11x+40=4x^2+16x-11}}}
{{{4x^2+5x-51=0}}}
{{{(x-3)(4x+17)=0}}}<br>
x = 3 or x = -17/4; of course the negative solution makes no sense in the problem.<br>
So the units digit is x=3 and the tens digit is x+4=7.<br>
ANSWER: 73<br>
CHECK:
product of digits: 7*3 = 21
4 times product of digits: 4*21 = 84
11 less than 4 times product of digits: 84-11 = 73<br>