Question

The sum of two numbers is the same as four times the smaller number. If twice the larger is decreased by the smaller, the result is 30. Find the numbers.

Answer 1

The two numbers are 6 and 18

Step-by-step explanation:

The given is:

• The sum of two numbers is the same as four times the smaller number
• If twice the larger is decreased by the smaller, the result is 30

We need to find the the numbers

Assume that the smaller number is x and the larger number is y

∵ The smaller number = x

∵ The larger number = y

∵ The sum of the two numbers is the same as four times the

   smaller number

- That means add the two numbers and equate the sum by four

   times x

∴ x + y = 4x

- Subtract both sides by x

∴ y = 3x ⇒ (1)

∵ Twice the larger number is decreased by the smaller number,

   the result is 30

- That means multiply y by 2 and subtract x from the product,

    then equate the difference by 30

∴ 2y - x = 30 ⇒ (2)

- Substitute y in equation (2) by equation (1)

∵ 2(3x) - x = 30

∴ 6x - x = 30

- Add like terms in the left hand side

∴ 5x = 30

- Divide both sides by 5

∴ x = 6

- Substitute the value of x in equation (1) to find y

∵ y = 3(6)

∴ y = 18

The two numbers are 6 and 18

Learn more:

You can learn more about the system of equation in brainly.com/question/2115716

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