X.

sixth parts of a certain number exceeds the difference of its sixth and ninth parts by $16$. Find the number.

4. There are two consecutive numbers, $x$ and $x+1$, such that one-half the larger exceeds one-third the smaller number by $10$. Find the numbers.

Exercise 56.

Ex. The sum of two numbers is $63$, and if the greater is divided by the smaller number, the quotient is $2$ and the remainder $3$. Find the numbers.

lint Let x = the greater number. lint Then 63 - x = the smaller number. Since the quotient = Dividend - RemainderDivisor,

and since, in this problem, the dividend is $x$, the remainder is $3$, and the divisor is $63-x$, we have

x - 363 - x = 2. lint Solving, x = 43.

The two numbers, therefore, are $43$ and $20$.

1. The sum of two numbers is $100$, and if the greater is divided by the smaller number, the quotient is $4$ and the remainder $5$. Find the numbers.

2. The sum of two numbers is $124$, and if the greater is divided by the smaller number, the quotient is $4$ and the remainder $4$. Find the numbers.