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

  B.  $3

Step-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:

We can use the last equation to write an expression for l:

  9l = 54 -3m . . . subtract 3m

  l = 6 -m/3 . . . . . divide by 9

Substituting 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 terms

Dividing by 3 gives

  4s +3m = 17

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  10s +6m +(6 -m/3) = 43

  10s + (5 1/3)m = 36 . . . . subtract 6, collect terms

  30s +16m = 108 . . . . . . multiply by 3

Dividing by 2 gives

  15s + 8m = 54

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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 13

The price of a medium glass of lemonade is $3.

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Most graphing calculators and available on-line calculators can make solving three equations in three unknowns trivially simple.

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step-by-step explanation: