Find Two Numbers by Difference and Quotient Calculator

Welcome to the free online calculator to find two numbers by difference and quotient. For example, the difference of two numbers is 55 and their quotient is 6. What are the numbers? Or, the difference of two numbers is 72 and the quotient is 10, 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 difference is denoted by d, and the quotient is q.

Now, we can get two equations

x – y = d………(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 = d

qy – y = d

(q – 1)y = d

y = dq – 1

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

x = qy = qdq – 1

Obviously, the formulas for these two numbers are

x = qdq – 1

y = dq – 1

Among them, d represents the difference of two numbers, and q represents the quotient of the two numbers.

Back to the two examples from the beginning.

The difference of two numbers is 55 and their quotient is 6. What are the numbers?

Use the formulas summarized above to calculate these two numbers

x = qdq – 1 = 6 * 556 – 1 = 3305 = 66

y = dq – 1 = 556 – 1 = 555 = 11

Verify that the two numbers are correct.

66 – 11 = 55

6611 = 6

Yes, this is correct.

So, the two numbers are 66 and 11.

Another example, the difference of two numbers is 72 and the quotient is 10, what are the two numbers?

Also calculated according to the formulas

x = qdq – 1 = 10 * 7210 – 1 = 7209 = 80

y = dq – 1 = 7210 – 1 = 729 = 8

Verify

80 – 8 = 72

808 = 10

Meet the conditions.

Therefore, the answer is 80 and 8.

In short, the problem of calculating two numbers based on the difference 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 difference 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.