Last year three friends went out for dinner at a restaurant in Kingston. The cost of two pizzas, three fried chicken and two servings of pasta was $ 1500. The cost of the two pizza, two fried chicken and four servings of pasta was $2000. The cost of five pizzas, four fried chicken and two servings of pasta is $2500. The friends only had $3500 in total to pay the bill and they ate 3 pizzas, six fried chicken and six servings of pasta. 1. Were the friends able to pay the bill? 11. If yes, how much change did they receive after paying the bill? II If no, how much more money was required to cover the bill? N.B. Use a Matrix method of your choice to answer the above problem. Marks will be given for clearly stating the meaning of each variable used
(a) 2p+3c+2q = 1500
(b) 2p+2c+4q = 2000
(c) 5p+4c+2q = 2500
so you want the value of
3p+6c+6q = 12/5 (a) + 3/5 (b) - 3/5 (c)
= 12/5 * 1500 + 3/5 * 2000 - 3/5 * 2500
= 3600+1200-1500 = 3300
so, yes, they had enough to pay the bill