One positive integer is 5 less than three times another .If their product is 78 ,find the two integers.

In these types of problems, when you have two numbers you're trying to figure out, your goal is usually to write down two different equations, then solve them simultaneously to find the two numbers.

Let's call the two numbers x and y (it doesn't matter which is which). The first sentence starts with "One positive integer is". Written in the language of algebra, that just means "x =". Pretty simple.

Continuing on, the next thing we see is "5 less than". That means that you're going to end up subtracting 5 from whatever comes next. That way, you'll end up with 5 less than whatever it is. In other words, it means that your algebra equation is going to have some other stuff (which we'll figure out next), followed by "- 5".

Now on to the other stuff: the sentence continues with "three times another". Well, the "three times" part is pretty straightforward. The word "another" should tell you that it's the other unknown number besides the one at the beginning. Since we started with "x =", this number must be "y". So "three times another" just means "3y".

So now let's put it all together:

x = 3y - 5

Now on to the second sentence: The first part you see is "their product". The word "their" should clue you in that we're now talking about both numbers, x and y. The word "product", of course, means that they're multiplied together. So translating this into algebra, we have "xy" (meaning x times y). Finally, we have "is 78". Once again, the word "is" means "=", so our second equation becomes

xy = 78

There. That wasn't so hard was it?

Now the last thing you have to do is solve the two equations. Can you do that part? If so, what do you get for your two numbers, x and y?