Find Two Numbers by Sum and Quotient Calculator

Welcome to the free online calculator to find two numbers by sum and quotient. For example, the sum of two numbers is 15 and their quotient is 4. What are the numbers? Or, the sum of two numbers is 99 and the quotient is 8, what are the two numbers? And so on.

How to solve such problems quickly? Is there any formula that can be used?

Okay, let’s start from scratch.

Assuming the two numbers are x and y, their sum is denoted by s, and the quotient is q.

Now, we can get two equations

x + y = s………(1)

xy = q………(2)

Simplify the second equation, let x be represented by y.

xy = q

x = qy

Substitute x = qy into the first equation and simplify.

x + y = s

qy + y = s

(q + 1)y = s

y = sq + 1

According to the relationship between x and y, we can calculate the value of x.

x = qy = qsq + 1

Obviously, the formulas for these two numbers are

x = qsq + 1

y = sq + 1

Among them, s represents the sum of two numbers, and q represents the quotient of the two numbers.

Back to the two examples from the beginning.

The sum of two numbers is 15 and their quotient is 4. What are the numbers?

Use the formulas summarized above to calculate these two numbers

x = qsq + 1 = 4 * 154 + 1 = 605 = 12

y = sq + 1 = 154 + 1 = 155 = 3

Verify that the two numbers are correct.

12 + 3 = 15

123 = 4

Yes, this is correct.

So, the two numbers are 12 and 3.

Another example, the sum of two numbers is 99 and the quotient is 8, what are the two numbers?

Also calculated according to the formulas

x = qsq + 1 = 8 * 998 + 1 = 7929 = 88

y = sq + 1 = 998 + 1 = 999 = 11

Verify

88 + 11 = 99

8811 = 8

Meet the conditions.

Therefore, the answer is 88 and 11.

In short, the problem of calculating two numbers based on the sum and quotient can be easily solved by applying the above formulas.

Of course, if you want to be lazy, you can directly use the free calculator available on our page to find two numbers by sum and quotient. The calculator omits all steps and gives the answer in milliseconds.

Next, we will introduce how to use the calculator.

Using the calculator is simple, follow these 3 steps:

Next, let’s look at some examples.