Question

The sum of two numbers is 37. if the larger is divided by the smaller, the qoutient is 3 and the remainder is 5. Find the numbers.

Answer 1

let a be the larger number and b be the smaller number.
a + b = 37
a/b = 3 with a remainder of 5.
3 with a remainder of 5 is the same as 3 + 5/b.
so you get:
a + b = 37
a/b = 3 + 5/b
multiply both sides of a/b = 3 + 5/b by b to get:
a = 3b + 5
replace a in the equation of a + b = 37 with 3b + 5 to get:
3b + 5 + b = 37
simplify to get:
4b + 5 = 37
subtract 5 from both sides to get:
4b = 32
divide both sides by 4 to get:
b = 8
since a + b = 37, this means that a must be equal to 29 because 29 + 8 = 37.
your bigger number is 29 and your smaller number is 8.
a/b becomes 29/8 which becomes 3 with a remainder of 5.
your solution is:
the larger number is 29 and the smaller number is 8.
I hope it help you....