Let's assume x= greater number and y= smallest number.
Given, a greater number is seven less than five times a smaller number. Which can be transformed into an algebraic equation as follows:
x= 5y-7 ..... (1)
Now the sum of two numbers is 41. So,
x+y= 41 ...(2)
Now we can plug in x=5y-7 in equation (2). So,
5y-7+y=41
6y-7=41
6y-7+7=41+7 Add 7 to each sides of the equation.
6y= 48
[tex] \frac{6y}{6} =\frac{48}{6} [/tex] Divide 6 to each sides.
So, y=8
Next step is to plug in y=8 in equation (1). So,
x=5(8)-7
=40-7
=33.
So, the numbers are 8 and 33.
