Question

The sum of two numbers is 84 the first is nine more than four times the second find the numbers

Answer 1

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

#LearnwithBrainly