Question

Three multiplied by the first number is equal to the second number plus 4. The second number is equal to one plus twice the third number. The third number is one less than the first number. What is the sum of all three numbers?

Answer 1

The first number is 3, the second number is 5, and the third number is 2. The sum of all three numbers is 10.

Step-by-step explanation:

Let's assign variables to the three numbers:

First number = x

Second number = y

Third number = z

Given: Three multiplied by the first number is equal to the second number plus 4:

3x = y + 4

Given: The second number is equal to one plus twice the third number:

y = 1 + 2z

Given: The third number is one less than the first number:

z = x - 1

We can substitute the value of z into the second equation:

y = 1 + 2(x - 1)

y = 1 + 2x - 2

y = 2x - 1

Substituting the value of y into the first equation:

3x = (2x - 1) + 4

3x = 2x + 3

3x - 2x = 3

x = 3

Now we can find the values of y and z:

y = 2x - 1 = 2(3) - 1 = 5

z = x - 1 = 3 - 1 = 2

The sum of all three numbers is x + y + z = 3 + 5 + 2 = 10.