Vince’s family runs three lemonade stands during local events. Each stand serves lemonade in small, medium, and large glasses. The table gives the number of glasses of each size sold in each stand. Small Medium Large Stand 1 small 12 medium 11 large 6 Stand 2 small 10 medium 6 large 1 Stand 3 small 0 medium 3 large 9 The total collected from each stand was: stand 1, $87; stand 2, $43; and stand 3, $54. What is the price of a medium glass of lemonade? A. $2 B. $3 C. $4.50 D. $5

Answer:   B.  $3Step-by-step explanation:Let s, m, l represent the prices of small, medium, and large lemonades, respectively. Three equations can be written based on the given revenue:12s +11m +6l = 8710s +6m +1l = 430s +3m +9l = 54We can use the last equation to write an expression for l:   9l = 54 -3m . . . subtract 3m   l = 6 -m/3 . . . . . divide by 9Substituting this into the first two equations gives ...   12s +11m +6(6 -m/3) = 87 . . . . . sub for l in first equation   12s +9m = 51 . . . . subtract 36, collect termsDividing by 3 gives   4s +3m = 17__   10s +6m +(6 -m/3) = 43   10s + (5 1/3)m = 36 . . . . subtract 6, collect terms   30s +16m = 108 . . . . . . multiply by 3Dividing by 2 gives   15s + 8m = 54__We can multiply the first of these by 15 and the second by -4, then add the results to eliminate the s variable.   15(4s +3m) -4(15s +8m) = 15(17) -4(54)   60s +45m -60s -32m = 255 -216 . . . . . eliminate parentheses   13m = 39 . . . . . collect terms   m = 3 . . . . . . . . divide by 13The price of a medium glass of lemonade is $3._____Most graphing calculators and available on-line calculators can make solving three equations in three unknowns trivially simple.