Two integers have a sum of 18. The second is 3 less than twice the first. Find the numbers.

Question

Please help me with this question I've been stuck on it for a while 

Answer 1

Hi Kaya!

The best way to do math word problems is to think of it as translating from a different language - only instead of from French to English - we are going to go from English to "Math!"

So... your problem says:

 

Two integers have a sum of 18. The second is 3 less than twice the first. Find the numbers.

 

First of all remember that integers are whole numbers - not fractions or decimals. They can be negative or positive but they are "round" numbers.

Okay, so two numbers have a sum of 18.

 

Let's call the numbers "x" and "y" --  translating from words to math, then, would look like this:

 

x + y = 18

 

No we have: "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! 

3          3

 

Hope that helps, Kaya!

 

 

Hope that helps, Kaya!