Martha is selling 60 packs of tennis balls. She has packs of orange tennis balls and packs of yellow tennis balls. The ratio of the number of orange packs to the number of yellow packs is four to one. Both the orange pack and the yellow pack of tennis balls are usually priced at six pounds. During a sale, the price of a pack of orange tennis balls is reduced by a third. Martha sells all 60 packs during a sale. Work out the total amount of money that Martha receives.
Let’s break this question down piece by piece. The first two numerical pieces of information we’re given are the total number of tennis balls and the ratio of orange packs to yellow packs. It’s sensible then to work out the number of orange packs and the number of yellow packs by sharing 60 in a ratio of four to one. There are two ways we can do this. Let’s consider both methods.
The first method is a three-step process. First, we decide how many parts in total we’re sharing the packs into. We work this out by adding the numbers in the ratio. Four plus one is equal to five. So we’re looking to share 60 into five parts.
The second step is to share 60 into these five parts. When we share in maths, we divide. 60 divided by five is 12. This tells us that each part is worth 12 packs.
Since we know then that one part is worth 12, the final step is to multiply the 12 by each part of our ratio. The first bit of the ratio is four. Four multiplied by 12 is 48, so there are 48 orange packs. The second part of our ratio is one. One multiplied by 12 is 12, so there are 12 yellow packs.
Remember, we can check this by adding 48 and 12 and ensuring it sums to the original amount of packs. 48 plus 12 is 60. So that’s a good way to check what we’ve done is correct so far.
Now let’s look at the second method. This method is to consider the ratio as two fractions. Since there are a total of five parts to this ratio — four plus one is five — the fraction of packs which are orange must be four-fifths and the fraction of packs which are yellow must be one-fifth.
Once we have this, we can find four-fifths of 60 and one-fifth of 60 to work out the exact number of orange and yellow packs, respectively. To find a fifth of 60, we simply divide 60 by five, which is 12. One-fifth of 60 is 12, so there are 12 yellow packs. To find four-fifths of 60, we multiply this number, which represents a fifth of 60, by four. 12 multiplied by four is 48.
Once again, we found that we have 48 orange packs and 12 yellow packs. Either of these methods is completely valid. It’s very much a matter of personal preference.
The next bit of information we’re given is that the price of one pack is usually six pounds. But the price of the orange pack is reduced by a third. To work out the sale price of the orange tennis balls, we’ll first work out one-third of six pounds. To work out a third of six, we divide six by three, which is two pounds.
Since the price is being reduced, we need to subtract that two pounds from six pounds. That gives us a sale price of four pounds. We know then that the 48 packs of orange tennis balls are being sold for four pounds each and the 12 packs of yellow tennis balls are being sold for six pound each.
We’ll need to multiply 48 by four and 12 by six to work out the amount of money that Martha receives for each type of tennis ball. We can use any formal written method to calculate 48 multiplied by four. Usually, the column method or grid method are the most popular.
Let’s look at the column method. Eight multiplied by four is 32, so we put the units part of this number in this column and we carry the three. Four multiplied by four is 16. And then when we add that three, we get 19, so 48 multiplied by four is 192. The total amount of money Martha receives for the orange packs of tennis balls is 192 pounds. 12 multiplied by six is 72 pounds, so the yellow balls sold for 72 pounds.
Then to work out the total amount she receives, we’ll add these two numbers, 192 plus 72. Two plus two is four. Nine plus seven is 16. So we put the six in this column and carry the one. Then one add zero is one. And then we add that extra one that we just carried to give us a total of 264. The total amount of money that Martha receives is 264 pounds.