Question 1091073

a weekend trip package to the beach includes a two night hotel stay and four meals. a week trip includes a seven night hotel stay and ten meals. the 2 night stay has a price of $439.94 and the seven night stay has a price of $1419.83. find the cost of one hotel stay and one meal
<pre>Let one night be H, and one meal, M
Then we get: 2H + 4M = 439.94____2(H + 2M) = 2(219.97)____H + 2M = 219.97____H = 219.97 - 2M --------- eq (i)
7H + 10M = 1,419.83 ------- eq (ii)	
7(219.97 - 2M) + 10M = 1,419.83	-------- Substituting 219.97 - 2M for H in eq (ii)
1,539.79 - 14M + 10M = 1,419.83	
 - 4M = - 119.96	
M, or cost of one meal = {{{highlight_green(matrix(1,3, (- 119.96)/(- 4), "=", "$29.99"))}}}
Cost to stay 1 night = {{{highlight_green(matrix(1,4, 219.97, "- 2(29.99)", "=", "$159.99"))}}}