Question

The first number is eight more than the second one. Three times the second number plus twice the first number is equal to 26. Find the numbers

Answer 1

Let us consider the second number would be $"x"$

The first number is eight more than the second one.

That is, the first number would be $"x+8"$

Three times the second number would be $"3x"$

Twice the first number would be $"2(x+8)"$

Now write the statement in mathematical form: "Three times the second number plus twice the first number is equal to 26"

$3x+2(x+8)= 26$

Solve this equation for x:

Distribute 2 in $x+8$, we get

$3x+2x+16=26$

Combine the like terms,

$5x+16=26$

Subtracting 16 on both sides,

$5x+16-16=26-16$

$5x=10$

Dividing 5 on both sides,

$x=10/5=2$

So the second number is $x=2.$

Now find the first number:

First number $= x+8=2+8=10.$

Thus the numbers are 10 and 2.