WEBVTT
00:00:01.600 --> 00:00:05.040
Martha is selling 60 packs of tennis balls.
00:00:05.040 --> 00:00:09.520
She has packs of orange tennis balls and packs of yellow tennis balls.
00:00:09.520 --> 00:00:14.600
The ratio of the number of orange packs to the number of yellow packs is four to one.
00:00:15.560 --> 00:00:20.960
Both the orange pack and the yellow pack of tennis balls are usually priced at six pounds.
00:00:22.120 --> 00:00:26.120
During a sale, the price of a pack of orange tennis balls is reduced by a third.
00:00:26.800 --> 00:00:29.440
Martha sells all 60 packs during a sale.
00:00:30.040 --> 00:00:34.160
Work out the total amount of money that Martha receives.
00:00:34.160 --> 00:00:37.360
Let’s break this question down piece by piece.
00:00:37.360 --> 00:00:46.680
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.
00:00:46.680 --> 00:00:55.680
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.
00:00:55.680 --> 00:00:57.600
There are two ways we can do this.
00:00:57.600 --> 00:01:00.200
Let’s consider both methods.
00:01:00.200 --> 00:01:03.040
The first method is a three-step process.
00:01:03.280 --> 00:01:08.720
First, we decide how many parts in total we’re sharing the packs into.
00:01:08.720 --> 00:01:12.120
We work this out by adding the numbers in the ratio.
00:01:12.120 --> 00:01:14.640
Four plus one is equal to five.
00:01:15.360 --> 00:01:20.000
So we’re looking to share 60 into five parts.
00:01:20.000 --> 00:01:23.840
The second step is to share 60 into these five parts.
00:01:24.760 --> 00:01:27.360
When we share in maths, we divide.
00:01:27.360 --> 00:01:29.600
60 divided by five is 12.
00:01:30.680 --> 00:01:35.600
This tells us that each part is worth 12 packs.
00:01:35.600 --> 00:01:43.120
Since we know then that one part is worth 12, the final step is to multiply the 12 by each part of our ratio.
00:01:44.240 --> 00:01:46.200
The first bit of the ratio is four.
00:01:46.760 --> 00:01:51.200
Four multiplied by 12 is 48, so there are 48 orange packs.
00:01:52.120 --> 00:01:54.440
The second part of our ratio is one.
00:01:54.640 --> 00:01:59.560
One multiplied by 12 is 12, so there are 12 yellow packs.
00:01:59.560 --> 00:02:05.640
Remember, we can check this by adding 48 and 12 and ensuring it sums to the original amount of packs.
00:02:05.640 --> 00:02:07.480
48 plus 12 is 60.
00:02:08.320 --> 00:02:12.560
So that’s a good way to check what we’ve done is correct so far.
00:02:12.560 --> 00:02:14.480
Now let’s look at the second method.
00:02:14.480 --> 00:02:18.040
This method is to consider the ratio as two fractions.
00:02:18.840 --> 00:02:30.720
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.
00:02:32.120 --> 00:02:40.520
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.
00:02:41.640 --> 00:02:47.400
To find a fifth of 60, we simply divide 60 by five, which is 12.
00:02:47.720 --> 00:02:51.800
One-fifth of 60 is 12, so there are 12 yellow packs.
00:02:52.720 --> 00:02:59.000
To find four-fifths of 60, we multiply this number, which represents a fifth of 60, by four.
00:02:59.800 --> 00:03:02.520
12 multiplied by four is 48.
00:03:03.280 --> 00:03:08.760
Once again, we found that we have 48 orange packs and 12 yellow packs.
00:03:09.000 --> 00:03:11.320
Either of these methods is completely valid.
00:03:11.320 --> 00:03:13.160
It’s very much a matter of personal preference.
00:03:14.560 --> 00:03:19.880
The next bit of information we’re given is that the price of one pack is usually six pounds.
00:03:19.880 --> 00:03:22.920
But the price of the orange pack is reduced by a third.
00:03:23.480 --> 00:03:29.040
To work out the sale price of the orange tennis balls, we’ll first work out one-third of six pounds.
00:03:29.680 --> 00:03:34.120
To work out a third of six, we divide six by three, which is two pounds.
00:03:35.000 --> 00:03:39.800
Since the price is being reduced, we need to subtract that two pounds from six pounds.
00:03:39.800 --> 00:03:42.560
That gives us a sale price of four pounds.
00:03:43.640 --> 00:03:54.160
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.
00:03:54.160 --> 00:04:01.800
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.
00:04:03.120 --> 00:04:07.400
We can use any formal written method to calculate 48 multiplied by four.
00:04:07.600 --> 00:04:11.240
Usually, the column method or grid method are the most popular.
00:04:11.240 --> 00:04:13.640
Let’s look at the column method.
00:04:13.640 --> 00:04:20.240
Eight multiplied by four is 32, so we put the units part of this number in this column and we carry the three.
00:04:21.360 --> 00:04:23.600
Four multiplied by four is 16.
00:04:23.600 --> 00:04:30.200
And then when we add that three, we get 19, so 48 multiplied by four is 192.
00:04:31.040 --> 00:04:36.920
The total amount of money Martha receives for the orange packs of tennis balls is 192 pounds.
00:04:37.920 --> 00:04:44.640
12 multiplied by six is 72 pounds, so the yellow balls sold for 72 pounds.
00:04:44.640 --> 00:04:51.800
Then to work out the total amount she receives, we’ll add these two numbers, 192 plus 72.
00:04:52.560 --> 00:04:55.200
Two plus two is four.
00:04:55.200 --> 00:04:57.080
Nine plus seven is 16.
00:04:57.080 --> 00:05:00.480
So we put the six in this column and carry the one.
00:05:00.480 --> 00:05:02.320
Then one add zero is one.
00:05:02.600 --> 00:05:07.880
And then we add that extra one that we just carried to give us a total of 264.
00:05:08.800 --> 00:05:13.560
The total amount of money that Martha receives is 264 pounds.