One number is 8 more than another. If the sum of the smaller number and twice the larger number is 46, find the two numbers.Let x = the first number

Answers

Answer 1

Answer:

x = 18 y = 10

Step-by-step explanation:

let the first number be x

let the second number be y

x = y + 8..... equation 1

2x + y = 46.... equation 2

x is the larger number

y is the smaller number.

Rearrange the equation and add equation 1 to equation 2.

x - y = 8

+ 2x + y = 46

-------------------

3x + 0 = 54

3x = 54

divide both sides by 3

x = 54/3

x = 18

Substitute x = 18 into equation 1

x = y + 8

18 = y + 8

collect like terms

y = 18-8

y = 10

Answer 2

The two numbers are 18 and 10

From the question, One number is 8 more than another

Let the first number be x and the second number be y

x = y + 8 ------ (1)

From the second statement, the sum of the smaller number and twice the larger number is 46

That is,

y + 2x = 46 ----- (2)

Now, we will solve the two equations simultaneously

From equation (1)

We have x = y + 8

Substitute this into equation (2)

y + 2x = 46

y + 2(y+8) = 46

Then, clear the bracket

y + 2y + 16 = 46

3y + 16 = 46

Collect like terms

3y = 46 - 16

3y = 30

∴ y = 30 ÷ 3

y = 10

Substitute the value of y into equation (1)

x = y + 8

x = 10 + 8

x = 18

∴ x = 18 and y = 10

Hence, the two numbers are 18 and 10

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