Let us consider the second number would be [tex] "x" [/tex]
The first number is eight more than the second one.
That is, the first number would be [tex] "x+8"
[/tex]
Three times the second number would be [tex] "3x" [/tex]
Twice the first number would be [tex] "2(x+8)" [/tex]
Now write the statement in mathematical form: "Three times the second number plus twice the first number is equal to 26"
[tex] 3x+2(x+8)= 26
[/tex]
Solve this equation for x:
Distribute 2 in [tex] x+8 [/tex], we get
[tex] 3x+2x+16=26 [/tex]
Combine the like terms,
[tex] 5x+16=26 [/tex]
Subtracting 16 on both sides,
[tex] 5x+16-16=26-16 [/tex]
[tex] 5x=10 [/tex]
Dividing 5 on both sides,
[tex] x=10/5=2 [/tex]
So the second number is [tex] x=2. [/tex]
Now find the first number:
First number [tex] = x+8=2+8=10. [/tex]
Thus the numbers are 10 and 2.
