Rana sells 192 cakes in the ratio small : medium : large = 7 : 6 : 11. medium cakes are worth double small ones and large cakes triple small ones. If the cakes go for £532.48 how much is a small cake worth

First we can work out the actual number of small medium and large cakes. To do this we first add the ratio numbers together7+6+11 = 24We then divide the number of total cakes by this ratio number 192/24 = 8Then use this number and multiply it by the original ratio nuumbers to see how many of each cake we really have 8* (7:6:11) = 56:48:88 We need to find a small cakes value, so we will use an algebraic term A. We know that a medium cake is worth double a small one so it can be written as 2A, and a large cake is worth triple so can be written as 3A. There are 56 small cakes 48 medium cakes and 88 large onesWe will write this as 56A, 48(2A) and 88(3A) so 56A + 96A + 264A= 416A We know that all of this is worth £532.48So to work out the value of a small cake we simply take the total value and divide it by 416£532.48/416 = £1.28 A small cake is therefore worth £1.28