Last month Mario bought 26 cups of coffee and 37 cups of tea

Last month Mario bought 26 cups of coffee and 37 cups of tea from the studio canteen. They cost him $44.23 altogether. Luigi bought 15 cups of coffee and 48 cups of tea and they cost him $47.32 altogether. How much do cups of tea and coffee cost in cents?

Solution

Let\'s assume cost of cups be x cents and cost of coffee cups cost y cents

Mario : 26x + 37y = 4423 ----(1)

Luigi : 15x + 48y = 4732 ----(2)

Solve the two equations to get x and y :

Multiply each equation by a number that will create opposite coefficients for x.

In this case we will multiply first equation by -15 and the second equation by 26.

After multiplying we have the following system:

390x555y = 66345

390x+1248y =123032

---------------- add the two equations we get :

y = 56687/693 = 81.80 = 82 cents

; x = 37220/693 = 53.71 = 54 cents

Tea cups cost 82cents and coffee cups costs 54 cents