The larger number is 20.
Let's denote the larger number as x and the smaller number as y .
According to the given information, one number is 4 more than the other, which can be expressed as the equation: x = y + 4
The sum of twice the larger number and five times the smaller number is 120:
Now, substitute the expression for x from the first equation into the second equation:
Distribute and combine like terms:
Subtract 8 from both sides:
Divide by 7:
y=16
Now, substitute the value of y back into the equation for x:
So, the correct solution is
and
The larger number is 20.