A tour group split into two groups when waiting in line for

A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 4 soft drinks for $29.40. The second group bought 7 slices of pizza and 6 soft drinks for $30.30. How much does one slice of pizza cost?

Solution

Let the price of a slice of pizza be $x and the price of a soft drink be $y.Then 8x + 4y = 29.40 or, 4x + 2y = 14.70...(1) and 7x + 6y = 30.30...(2) On multiplying both the sides of the 1st equation by 3, we get 12 x + 6y = 44.10...(3). Now, on subtracting the 2nd equation from the 3rd equation, we get 12 x + 6y - 7x - 6y = 44.10 - 30.30 or, 5x = 13.80 so that x = 13.80/5 = 2.76. On substituting x = 2.76 in the 1st equation, we get 4 *2.76 + 2y = 14.70 or, 2y = 14.70 - 11.04 = 3.66 so that y = 3.66/2 = 1.83. We can verify the result by substituting x = 2.76 and y = 1.83 in the 2nd equation. Then. we get, 7 * 2.76 + 6*1.83 = 30.30 or, 19.32 + 10.98 = 30.30 , which is correct. Thus the price of a slice of pizza is $ 2.76 and price of a soft drink is $ 1.83