Video: AF5P3-Q10-576193694605

A pottery house needs to produce 630 mugs and 320 vases each week. In 1 day, a potter can produce 21 mugs or 8 vases. Each potter works for 5 days a week. (a) Work out the minimum number of potters needed to meet the target. (b) The pottery house alters the size of its products, which results in the following changes. Each day, a potter increases their mug production by 1/7 or decreases their vase production by 1/4. Each mug requires 400 g of clay to produce. Each vase requires 2.5 kg of clay to produce. The manager does a calculations.

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Video Transcript

A pottery house needs to produce 630 mugs and 320 vases each week. In one day, a potter can produce 21 mugs or eight vases. Each potter works for five days a week. Part a) Work out the minimum number of potters needed to meet the target.

There’s also a part b that we’ll come to in a bit. So we’re told that in one day a potter can produce 21 mugs or eight vases, and a potter works five days a week. So therefore, what we want to do is work out how much each potter can produce in a week. We’re gonna start with mugs. So we’re gonna see how many mugs a potter could produce in a week. Well, our mugs per potter per week is gonna be equal to 21 because that’s the number of mugs that a potter can produce in a day multiplied by five because that’s the number of days a potter works in a week. And this is gonna give us a total of 105. So therefore, we know that one potter can produce 105 mugs per week.

So therefore, we can work out how many potters required to produce the 630 mugs that the pottery house needs to produce. So therefore, if we want to work out, the number of potters required to make 630 mugs, what we’re going to do is divide the 630 mugs that need to be produced by 105. And that’s because we know that a potter can produce 105 mugs in a week. Well, this is equal to six. So we can say that six potters are required to produce the 630 mugs that are needed for the pottery house. Well, have we solved the problem? And the answer is no, because what we need to do now is look at the vases cause we’ve only dealt so far with the mugs.

Well, the first thing we need to do is once again work out how many vases a potter can make per week. Before we looked at mugs per potter per week, now we’re looking at vases per potter per week. Well, we know that one potter can make eight vases in one day. So therefore, we’re gonna have to work out how many they can make in five days cause that’s how many days they work. So to work that out, what we’re gonna do is do eight multiplied by five. And that’s because obviously we know that a potter produces eight vases in a day and works for five days a week. And this is gonna give us an answer of 40. So therefore, we can say that a potter produces 40 vases per week.

So now, what we need to do is work out how we meet the demands of the pottery house. And we know that the pottery house needs to produce 320 vases each week. Well, if we want to work out the number of potters required to make 320 vases, what we’re gonna need to do is divide 320 because that’s the total number of vases required by 40 and that’s because that’s the number of vases per potter per week, which will give us an answer of eight potters. So we know that eight potters are required each week to make 320 vases.

Well, what we’re trying to do now is work out the final answer. The final answer wants us to find the minimum number of potters needed to meet the target. Now, a key word here is the word “or” because what we’re told is that a potter can produce 21 mugs “or” eight vases. They can’t do both. So therefore, we’re gonna have to have the six potters to make the mugs and the eight potters to make the vases. So therefore, the minimum number of potters required is gonna be equal to eight plus six, which gives a total of 14 potters. So therefore, we’ve worked out the answer to part a because 14 potters are required to meet the target of the pottery house.

So now, we can move on to part b. So for part b), we’re told that the pottery house alters the size of its products, which results in the following changes. Each day, a potter increases their mug production by one-seventh or decreases their vase production by a quarter. Each mug requires 400 grams of clay to produce. Each vase requires 2.5 kilograms of clay to produce. The manager does the following calculations. One day of mugs for one potter, a seventh increase in mug production equals 21 plus three, which is equal to 24 mugs. Clay needed for mug production is equal to 24 multiplied by four, which is equal to 96 kilograms. For one day of vases by one potter, we’ve got a quarter decrease in vase production, which is equal to eight minus four which is equal to four vases. Clay needed for vase production, therefore, is equal to four multiplied by 2.5, which equals 10 kilograms. The total materials for one day for one potter on mugs and one potter on vases, well, the total clay needed is equal to 96 kilograms plus 10 kilograms, which is equal to 106 kilograms.

So now, what we need to do is check the manager’s working and correct any mistakes. And then, we’re gonna write any of the correct calculations in the table we’ve got here. So before we start to check the calculations, we need to remind ourselves that one potter can produce either 21 mugs or eight vases per day. We’re gonna start with the first calculation. And the first calculation is trying to calculate the one-seventh increase in mug production. So if we’re looking for one-seventh of 21, well this is the same as one-seventh multiplied by 21. And we can either type this into our calculator or divide 21 by seven, which will give us three, which is the correct value that’s been used in the table. So therefore, the new amount is gonna be equal to 21 plus three, which is 24 which is what we’ve been given in the calculations that the manager has done. So that’s correct. So our first row is correct.

So now, what we can do is move on to the second row and we’re looking at the clay needed for mug production. Well, the first calculation is 24 multiplied by four. Is this correct? Let’s have a look at the amount of clay that’s needed for each of our mugs. We’re told that each mug requires 400 grams of clay. Well, we have a conversion that we know that can help us with this because we know that one kilogram is equal to 1000 grams. Well, therefore, we can say that 400 grams as kilograms is gonna be equal to 400 divided by 1000 which is gonna be equal to 0.4 kilograms. And we could do this again with a calculator.

Or if we’re dividing by 1000, what this means is that each of our digits is gonna move three place values to the right. So our four goes from hundredths to tenths. So we get 0.4 kilograms. Well, we can see that this is wrong in our table. Because in our table, we have 24 multiplied by four, not 0.4. So therefore, we can work out the actual clay needed. And it’s gonna be 24 multiplied by 0.4, which gives a total of 9.6 kilograms, which therefore tells us that the second row is incorrect. So we can now write in our corrections.

So now with that row corrected, we could move on to the vases. And with the first row of vases, we’re told that a quarter decrease in vase production is equal to eight minus four which is equal to four vases. Well, let’s check that. We’ve got a quarter of eight, which is the same as a quarter multiplied by eight or eight divided by four. Well, this is in fact two. So therefore, this means that our decrease in vases is two and not four as in the table. So therefore, we can say that the new vase production must be equal to eight, which was the original amount minus two, which is equal to six. So this row is incorrect. So what I’m gonna do now is write in my corrections. We know that this row must also be incorrect because we carry through the wrong value because we carry through the four. But let’s check to see if the rest of it is correct.

Well, we’re told that the clay needed for vase production is four multiplied by 2.5, which is equal to 10 kilograms. We already discussed the four is incorrect. So therefore, we can say that the clay needed is gonna be equal to six because that’s the number of vases that we’ve now calculated multiplied by 2.5, which is correct because 2.5 kilograms is the amount of clay needed to produce each vase. So that’s gonna give us a value of 15 kilograms. So as we already know, that row was incorrect. So now, we can write in the corrections.

So now with those written in, we can move on to our final part, which is the total clay needed. Well, we’re told that the total clay needed is equal to 96 kilograms plus 10 kilograms which is equal to 106 kilograms. Well, we know that this is incorrect. The calculation is the correct calculation. However, the values are not. Because we know that instead of 96 kilograms, we have 9.6 kilograms of the clay needed for mug production. And instead of 10 kilograms, we have 15 kilograms of the amount of clay needed for vase production. So the calculation we should have for the total clay needed is gonna be equal to 9.6 plus 15 which gives us the total amount of clay that’s required of 24.6 kilograms. So therefore, we know that this row is definitely incorrect and I can write in the corrections.

So therefore, we’ve answered the question fully because we’ve worked out all the corrections that are required from the manager’s calculations. And we found that the total clay needed is equal to 24.6 kilograms.

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