Here is a rule for the time it takes to cook a chicken. Cooking time equals 20 minutes plus an extra 40 minutes for each kilogram. How many minutes will it take to cook a three-kilogram chicken? Then there is a second part to the problem: what is the mass of a chicken that takes 100 minutes to cook?
In this problem, we’re given a rule that tells us how long to cook a chicken for. This is not just made up for a maths problem. These sorts of rules can be found on packets of meat when you buy them in the shops. The rule is that a chicken takes 20 minutes plus an extra 40 minutes for each kilogram.
The first part of the problem gets us to apply this rule. It asks us to calculate the cooking time for a three-kilogram chicken; how many minutes will it take to cook? The important fact in this sentence is the mass of the chicken, three kilograms. We know that the cooking time will be 20 minutes plus 40 minutes for each kilogram. We know there are three kilograms. So that’s three lots of 40.
A number sentence like this that has got a multiplication and addition in it, we always work out the multiplication first. What’s 40 multiplied by three? Well, we know that four threes are 12. So 40 threes must be equal to 120. So the 40 minutes for each of the three kilograms comes to 120 minutes. Now, we need to add it to the original 20 minutes. 20 plus 120 equals 140. This represents 140 minutes.
We could try to convert this into hours and minutes. It’s the same as two hours and 20 minutes. But be careful; that’s not what the question asks us to do. It asks us how many minutes. So we need to give our answer in minutes. And so, a three-kilogram chicken will take 140 minutes to cook.
The next part of the problem describes a chicken that takes 100 minutes to cook. And we’re asked to find the mass of this chicken. There are two ways we could find the answer to this question: one is quick and the other is really quick. Let’s go through the quick method first of all.
We know that the 100 minutes that it takes the chicken to cook is made up of 20 plus however many 40s we need, depending on how heavy the chicken is. If the chicken only weighed one kilogram, then our calculation will be 20 plus 40 which takes us to 60 minutes. So that’s not equal to 100 minutes.
What if the chicken weighed two kilograms? 40 minutes for each kilogram is 40 times two, which is 80 minutes. 20 plus 80 equals 100. So we know the mass of the chicken must be two kilograms. That was the quick method.
Here’s the really quick method. We know from our answer to the first part of the problem that it takes 140 minutes to cook a three-kilogram chicken. Now, we’re being asked about a chicken that takes 100 minutes to cook which is 40 minutes less. We know from the rule that 40 minutes equals every extra kilogram. So if we cook the chicken for 40 minutes less, that means there must be one less kilogram — different method, same-size chicken.
To solve both parts to the problem, we had to apply the cooking rule that we were giving. And so, we know a three-kilogram chicken will take 140 minutes to cook. And a chicken that takes 100 minutes to cook has a mass of two kilograms.