Adam buys six bags of white balloons. Chen buys three bags of red balloons. Adam says, “I have four times as many balloons as Chen.” Explain why Adam is correct.
In this problem, we need to find an explanation why Adam has four times more balloons than Chen. Let’s look at what they buy. We’re told that Adam buys six bags of the white balloons. And we can see that each pack of white balloons contains 24 balloons. So the total of balloons that Adam buys is six multiplied by 24. Six is the number of bags, and 24 is the number of balloons in each bag.
What do we know about Chen? Well, we’re told that Chen buys three bags of red balloons. We know from the picture that each pack of red balloons contains 12 balloons. So the multiplication that we’d need to work out to find out how many balloons Chen bought is three multiplied by 12. The number of bags is three, and the number of balloons in each bag is 12.
Now we don’t need to calculate these answers. We simply need to explain why Adam’s right when he says that he’s bought four times as many balloons as Chen. Let’s start by comparing the number of bags that each person buys. Adam buys six bags of balloons. Chen only buys three bags of balloons. So we can say that Adam buys twice as many bags.
Now let’s compare the amount of balloons that are in each of their bags, because they’re different too. Chen has 12 balloons per bag, and Adam has 24 balloons per bag. Not only does Adam buy twice as many bags, but each of his bags contain twice as many balloons. 12 doubled is 24. And so we know that if there are twice as many bags and each bag contains twice as many balloons, multiplying by two and then by two again is the same as multiplying by four. And so that’s how Adam knows that he has four times as many balloons as Chen.
Now we need to just write this as an explanation. How do we know Adam is correct? Well, because Adam buys twice as many bags. His bags each contain twice as many balloons. So Adam buys two times two or four times as many balloons as Chen.