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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