Video: Interpreting Remainders to Solve Word Problems

One bag of rabbit food will feed James’s rabbits for 20 days. How many bags are needed to feed his rabbits for 8 weeks?

03:31

Video Transcript

One bag of rabbit food will feed James’s rabbits for 20 days. How many bags are needed to feed his rabbits for eight weeks?

The first piece of information that we’re told in this problem is that one bag of rabbit food is enough to feed James’s rabbits for 20 days. And we need to find out how many bags are needed to feed his rabbits for eight weeks. At the moment, we can see that the two units of measurement that we’re talking about are different, 20 days and eight weeks. To help us find the answer, we’re going to have to convert one of them so that they’re both in the same units of measurement. And the quickest one to change is eight weeks.

How many days are in eight weeks? We know that one week equals seven days. And so eight weeks is the same as eight times seven days. We know eight times seven equals 56. So eight weeks is the same as 56 days. Now that both lengths of time are in the same units of measurement, we can find the answer. If one bag of rabbit food feeds James’s rabbits for 20 days, then we need to find out how many lots of 20 days there are in 56 days. What is 56 Divided by 20? We know one times 20 equals 20 and two 20s are equal to 40. This is as close as we can get to 56 because three 20s will take us to 60 which is greater than 56. So there are only two 20s in 56 but there’s a remainder.

What’s the difference between 40 and 56? The difference or the remainder is 16. And we need to pause here and think about what this remainder represents. We’ve divided 56 days by chunks of 20 days. And so the number 16 that we have a remainder is a number of days. These are the days from day 40 up to day 56. And if we only look at the whole number and only give James’s rabbits two bags of rabbit food, then they’ll have these 16 days without any food. We’re going to have to give them another bag. And so a question like this that has a remainder, we need to round up to the nearest whole number. So instead of two remainder 16, we have to say the answer is three. James is going to need three bags of rabbit food to feed his rabbits for eight weeks.

We started off by calculating that eight weeks was the same as 56 days. We knew that one bag of rabbit food would feed James’s rabbits for 20 days, so we needed to divide 56 by 20 to see how many bags he needed. The answer was two remainder 16. Two bags would feed his rabbits for 40 days, but there was another 16 days left over. So we rounded our remainder to the nearest whole number. The number of bags that James needs to feed his rabbits for eight weeks or 56 days is three bags.

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