Alice and Bob each own a cake shop. The table shows information about cake sales and number of employees in January and June of the same year. Part a) Work out the percentage decrease in sales from January to June for Alice’s shop.
Which bits of information in the table are relevant for answering this part of the question? We’re only interested in Alice’s shop. And in particular, we’re interested in the sales, the percentage decrease in sales from January to June.
We see that the sales are given in the hundreds of pounds and that for January the sales were 21 hundred pounds and for June they were 18.5, again in units of hundred pounds. These are the values from the table that we need to answer this part of the question. Let’s erase the wording of part b) so that we have space to work with these values.
Writing these values down then, the sales in January were 21 in units of hundred pounds and the sales in June were 18.5 in units of hundred pounds. We can work out in our heads or using a calculator that 21 hundreds of pounds is 2100 pounds and similarly that 18.5 hundreds of pounds is 1850 pounds.
Okay, let’s clear some more room. What do we do with these values? We’re interested in the percentage decrease in the sales from January to June. We can see that sales decreased from January to June. They took 2100 pounds in January and only 1850 pounds in June, and so there is a decrease of 2100 pounds minus 1850 pounds. But remember, we’re interested in this decrease as a percentage. But a percentage of what?
Well, we always give a percentage increase or decrease as a percentage of the initial value. And as January comes before June, our initial value is 2100 pounds, the sales in January. And so we need to divide through by this value. Now of course the units of pounds don’t really matter, and we have an expression we can put into our calculator. We get 0.11904, and so on. The decimals keep coming.
But remember, we want this as a percentage. And so we have to multiply this decimal by 100 to get the number of percent, or alternatively we can use some functionality of our calculator. Rounding to three significant figures then, we get 11.9 percent. Let’s clear some room so we can attempt part b.
Part b) asks which shop had more sales per employee in January. You must show how you got your answer.
We’re interested in information from January, so we only need to worry about data in this row of the table. And we’re interested in the sales per employee for each shop. So for each shop, we should take the amount of sales in pounds and divide that by the number of employees.
In January, Alice’s shop had 21 hundreds of pounds in sales, and these sales were divided between five employees. So we divide this value by five. Using our calculator, we find that 21 divided by five gives 4.2, and of course this is in units of hundreds of pounds, and 4.2 hundreds of pounds is 420 pounds. We would have got the same answer if we’d written 21 hundreds of pounds as 2100 pounds. Alice’s shop therefore made 420 pounds of sales per employee in January.
We do the same calculations for Bob’s shop using the data for his shop. So there are 97 hundred pounds of sales in January, split between 21 employees. Putting this into our calculator, we get 4.619 dot dot dot in units of hundreds of pounds, which is 462 pounds per employee to the nearest pound.
So which shop had more sales per employee in January? Well, 462 pounds is greater than 420 pounds, and so Bob’s shop had more sales per employee in January.