The sum of two numbers is 48. The larger number is 7 less than four times the smaller number. Find the numbers.

x = 37 and y = 11

Explanation:

Let x be the bigger number
Let y be the smaller number

x + y = 48

But x is 7 less 4 times the smaller number.

=> x = 4y - 7
Substitute this value of x:

4y - 7 + y = 48
5y = 48 + 7
5y = 55
y = 11

Substitute the value of y in to the equation:

x + 11 = 48
x = 48 - 11
x = 37

Therefore, x = 37 and y = 11