Question

Sam and Larry’s Ice Cream Shoppe sells the following sizes of ice cream cones: single at $0.89, double at $1.19; triple at $1.39. One day, Danielle sold 52 ice cream cones. She sold two more than twice as many doubles as triples. If she sold $58.98 in cones, how many of each size did she sell?

Answer 1

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Answer:

• 17 singles
• 24 doubles
• 11 triples

Step-by-step explanation:

Let s, d, t represent the numbers of singe, double, and triple cones sold. The problem statement tells us three relationships.

  s + d + t = 52 . . . . . . Danielle sold 52 cones one day

       d -2t = 2 . . . . . . . doubles is 2 more than twice the number of triples

  0.89s +1.19d +1.39t = 58.98 . . . . total amount of sales

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There are many ways to solve this set of equations. A graphing calculator can quickly tell you the solution is ...

  (s, d, t) = (17, 24, 11)

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If you want to solve this by hand, it may work well to use substitution.

The second equation gives an expression for d:

  d = 2t +2

The first equation gives an expression for s that can be written in terms of t.

  s = 52 -d -t

  s = 52 -(2t +2) -t = 50 -3t

Using these in the last equation, we have ...

  0.89(50 -3t) +1.19(2t +2) +1.39t = 58.98

  1.10t = 12.10 . . . . . . . . collect terms, subtract 46.88

  t = 11 . . . . . . . . . . . . . . divide by 1.10

  d = 2(11) +2 = 24

  s = 50 -3(11) = 17

Danielle sold 17 singles, 24 doubles, and 11 triple cones.