Question

Two numbers have a sum of 18. The first number is 2 more than 3 times the second number. Find the two numbers.

Smaller = ?

Larger = ?

Answer 1

Answer:y=2x-3 and x=7

Step-by-step explanation: x + y = 18

"The second is 3 less than twice the first."

SO that looks like:

the second ("Y") "is" always means "equals" and then 3 less - means we subtract 3, and then twice the first means 2 times the "x"

So we end up with:

y = 2x - 3

Now we also know that we can only solve an equation with ONE variable in it, BUT we have an "x" and a "y!" But the good thing is that if we have an equation with an equals sign in the middle, we can substitute either side of the equation in for that variable in another equation. So....

we have now:

x + y = 18, and

y = 2x - 3

so taking what comes after the "y =" part above, we can substitute that into the first equation to get this:

x + (2x - 3) = 18

Now we have only one variable - X, and we can solve for x! Rearranging our parentheses from the above equation, we can get:

(x + 2x) - 3 = 18, or 3x - 3 = 18.

Then we can get:

3x = 21

then we divide BOTH sides by 3 to get:

3x = 21, or 7! So X = 7!