It costs a total of R138.90 to purchase 10 loaves of bread and 12 litres of cooidrinks in a store. If the store raises the price of bread by 20% and the price of cooldrinks by 10%, the total price of these items becomes R159.54. Find the original price of three loaves of bread and two litres of cooldrinks. ​

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  R32.15

Step-by-step explanation:

Let x and y represent the original price of a loaf of bread and a liter of drink, respectively. The two relations given by the problem statement are ...

  10x +12y = 138.90

  10(1.2x) +12(1.1y) = 159.54

Multiplying the first equation by 1.2 and subtracting the second gives ...

  1.2(10x +12y) -(10(1.2x) +12(1.1y)) = 1.2(138.90) -(159.54)

  1.2y = 7.14 . . . . collect terms

  y = 5.95 . . . . . divide by 1.2

The value of x can be found from the first equation.

  10x + 12(5.95) = 138.90

  10x = 67.50 . . . . . . . . . . . subtract 71.40

  x = 6.75 . . . . divide by 10

Then the value of 3x+2y is ...

  3(6.75) +2(5.95) = 32.15

The original price of 3 loaves and 2 liters is R31.15.

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