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Maria and Javier are taking a trip to a crafts store to buy supplies for an arts project. Maria buy 11 packs of ribbon and 16 neon markers for a total of $6.23. Javier buys 13 packs of ribbon and 7 neon markers for a total of $6.41.

Write a system of equations to represent the cost of the ribbon, r and markers, m.

Solve your system to determine the cost of each item.

Respuesta :

sqdancefan

Answer:

  • ribbon: $0.45
  • markers: $0.08

Step-by-step explanation:

Each purchase will be the sum of products of item price and number of items. The two purchases give rise to two equations.

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equations

The variables are defined in the problem statement. The two purchases are ...

  11r +16m = 6.23

  13r +7m = 6.41

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solution

A calculator offers a simple way to find the solutions to these equations. The attachments show the solution to be ...

  • r = 0.48
  • m = 0.08

The cost of ribbon is $0.45; the cost of a marker is $0.08.

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The "cross-multiplication" method of solving these equations seems particularly useful when the coefficients are mutually prime. It starts with a rewrite to general form:

  • 11r +16m -6.23 = 0
  • 13r +7m -6.41 = 0

Then we define three "cross products":

Δ1 = (11)(7) -(13)(16) = -131

Δ2 = (16)(-6.41) -(7)(-623) = -58.95

Δ3 = (-6.23)(13) -(-6.41)(11) = -10.48

The solutions are ...

  r = Δ2/Δ1 = -58.95/-131 = 0.45

  m = Δ3/Δ1 = -10.48/-131 = 0.08

The cost of ribbon is $0.45; the cost of a marker is $0.08.

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For more about the cross-multiplication method you can read ...

https://brainly.com/question/26397343

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