Answer:
The numbers are 4, 8 and 14
Step-by-step explanation:
Required
Determine the three numbers
We start by declaring the variables
Let the three numbers be [tex]x,\ y\ and\ z\ respectively[/tex]
Next, we write the relationships between the numbers
[tex]y = 2 * x[/tex] --- Second = Twice the first
[tex]z = 6 + y[/tex] --- Third = 6 more than second
[tex]x + y + z = 26[/tex] --- Sum of the three numbers
Then, we solve for each number
[tex]y = 2 * x[/tex]
[tex]z = 6 + y[/tex]
[tex]x + y + z = 26[/tex]
Substitute 6 + y for x in [tex]x + y + z = 26[/tex]
[tex]x + y + 6 + y =26[/tex]
Collect Like Terms
[tex]x + y + y = 26 - 6[/tex]
[tex]x + 2y = 20[/tex]
Substitute 2 * x for y in [tex]x + 2y = 20[/tex]
[tex]x + 2(2*x) = 20[/tex]
[tex]x + 4*x = 20[/tex]
[tex]x + 4x = 20[/tex]
[tex]5x = 20[/tex]
Solve for x
[tex]x = \frac{20}{5}[/tex]
[tex]x = 4[/tex]
Recall that:
[tex]y = 2 * x[/tex]
[tex]y = 2 * 4[/tex]
[tex]y = 8[/tex]
Recall that:
[tex]z = 6 + y[/tex]
[tex]z = 6 + 8[/tex]
[tex]z = 14[/tex]
Hence, the numbers are 4, 8 and 14
To test the result:
[tex]x + y + z = 26[/tex]
[tex]4 + 8 + 14 = 26[/tex]
[tex]26= 26[/tex]
