Video: KS2-M18 • Paper 3 • Question 15

A shop prints designs on T-shirts. They use this formula to work out the price for printing a design. Price = 60 p × number of colours + £1.25. What is the price, in pounds, for printing a design that has 3 colours in it? Amina has £5 to spend on printing a design. What is the greatest number of colours she can have in the design?

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Video Transcript

A shop prints designs on T-shirts. They use this formula to work out the price for printing a design. Price equals 60 pence times the number of colours plus one pound 25. What is the price, in pounds, for printing a design that has three colours in it?

So we know the formula is 60 pence times the number of colours. And we’re told that Amina’s design has three colours. And then we have to add one pound 25. So we need to multiply 60 pence by three. And then, add one pound 25. 60 times three is 180 or 180 pence. We can write that in pounds as one pound 80. So to calculate the cost of Amina’s design with three colours, we need to add one pound 80 and one pound 25. One pound plus one pound equals two pounds. 80 pence and 20 pence makes a pound. So now we have three pounds. So we just need to add the five. The cost of a T-shirt with three colours is three pounds and five pence.

Now we can answer the second part of the question. We need to calculate how many colours Amina can have in her design. So we have five pounds to start with. And we know that we calculate the cost of the colours by multiplying 60 pence by the number of colours. And then we have to add one pound 25. So if we take one pound 25 from five pounds, that will tell us how much money Amina has left for printing her colours. Five pounds take away one pound 25 is 3.75.

To calculate how many colours Amina can afford, we need to divide three pounds 75 by 60 pence. To do this, we need to convert pounds into pence. Then, we can calculate 375 pence divided by 60 pence. Or, how many 60 pences there are in 375 pence. We already know that six times six is 36. So six times 60 is 360 pence. And 375, which is how much money Amina has got to spend, take away the cost of six colours, which is 360, leaves Amina with 15 pence left over.

We know the price of one colour is 60 pence. So this 15 pence is not enough to buy another colour. So 375 pence divided by 60 pence equals six with a remainder of 15. So Amina can afford to pay for six colours in her design.

We calculated the cost for printing a design that has three colours in it using the formula given. The price equals 60 p times the number of colours plus one pound 25. So a design with three colours is 60 p times three, which is 180 pence or one pound 80, plus one pound 25. So the cost of Amina’s design was three pounds and five pence.

To work out how many colours Amina could afford to pay for in her design using her five pounds, first we subtracted one pound 25 from five pounds which left Amina with three pounds 75 to spend on the colours in her design. We know the price of one design is 60 pence. So we divided three pounds 75 or 375 pence by 60 which gave us six with a remainder of 15 pence. This means Amina could afford to pay for six colours in her design.

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