The product of twenty less than a number and the number.

Question

i am very bad at word problems and need major help with them for my math class.

Answer 1

Word problems require you to find the question & convert it into math symbols. Many students have difficulty with this, so don't feel bad about it. All it takes is some logical thinking, some discernment, a little stubbornness or cleverness, and plenty of practice. You can definitely improve by working problems all the time. There are no wrong answers - only learning experiences!

Always try to find WHAT it IS asking, what it's NOT ASKING, and how you might represent words & phrases using math symbols. Then sift through the problem to find what you need & how to represent it, and ignore what you don't need.

Because the numbers in this problem are unknown, we use variables to represent them. In this case, we're dealing with "a number", which we can call x or a or z (doesn't matter). Let's use x. The other number is "20 less than" that, so we call it x-20. Make sense?

Now, multiply them:

x(x-20)=x•x + x•-20

           = x^2 + -20x

           = x^2 - 20x

 

x^2 is the same as saying "x squared". Many devices don't allow us to write superscript.

 

I hope that helps!

Answer 2

we don't know what "the number" is so let's call it X

 

when we talk about "the product" of two numbers we mean the answer when you multiply the two numbers. So in word problems the word product means you will multiply.

 

twenty less than a number means the number minus 20.

 

So now we're ready to write the mathematical expression from the English sentence.

 

x is a number

x - 20 is twenty less than a number

the product is   x(x - 20)

 

I put x - 20 in parentheses because it has two terms separated by the minus sign and BOTH terms need to be multiplied by x.

 

If you distribute x(x - 20) you get x² - 20x

 

If I had written incorrectly   x*x - 20, I would have x² - 20 which is not the same as x² - 20x