The sum of two numbers is 40 . One number is 4 times as large as the other. What are the numbers?

Solution:

Let the two numbers be x and y

Let us express the given statements algebraically.

Step1:

Given that the sum of the two numbers is 40

⇒ x + y = 40 -- (1)

Step2:

Also given that one number is 4 times as large as the other.

Assume x is 4 times larger than y

⇒ x = 4y --- (2)

Step3 :

From equations (1) and (2) we can find the values of x and y.

Replace equation (2) in equation (1)

⇒ 4y + y =40

⇒ 5y = 40.

⇒ y = 40/5

y = 8

Step4:

Replace the value of y = 8 in equation (2) to find the value of x

Therefore, x = 4 × 8 = 32.

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The sum of two numbers is 40. One number is 4 times as large as the other. What are the numbers?

Summary:

If the sum of two numbers is 40 and one number is 4 times as large as the other, then the two numbers are 8 and 32

Verification:

8 + 32 = 40 and 32 = 4× 8.