The numbers are 69 and 15
Step-by-step explanation:
The given is:
- The sum of two numbers is 84
- The first is nine more than four times the second
We need to find the two numbers
Assume that the 1st number is x and the 2nd number is y
∵ The sum of the two numbers are 84
∵ The 1st number is x and the 2nd number is y
- Add x and y, then equate the sum by 84
∴ x + y = 84 ⇒ (1)
∵ The first is nine more than four times the second
- Multiply y by 4 and add the product to 9, then equate
the sum by x
∴ x = 4y + 9 ⇒ (2)
Now we have a system of equations to solve it
Substitute x in equation (1) by equation (2)
∵ (4y + 9) + y = 84
- Add the like terms in the left hand side
∵ (4y + y) + 9 = 84
∴ 5y + 9 = 84
- Subtract 9 from both sides
∴ 5y = 75
- Divide both sides by 5
∴ y = 15
- Substitute the value of y in equation (2) to find x
∵ x = 4(15) + 9
∴ x = 60 + 9
∴ x = 69
The numbers are 69 and 15
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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