+165 Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 4/3 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
+10 Let the numbers be \(x-3,x-2,x-1,x,x+1,x+2,x+3\)
Their sum is
\(7x=\frac{4}{3}(x+3)\)
Solving we get:
\(x=\frac{12}{17}\)
The largest number is \(x+3=\frac{12}{17}+\frac{3}{1}=\boxed{\frac{63}{17}}\)
Which is not an integer and the question is flawed.
+10 Let the numbers be \(x-3,x-2,x-1,x,x+1,x+2,x+3\)
Their sum is
\(7x=\frac{4}{3}(x+3)\)
Solving we get:
\(x=\frac{12}{17}\)
The largest number is \(x+3=\frac{12}{17}+\frac{3}{1}=\boxed{\frac{63}{17}}\)
Which is not an integer and the question is flawed.
