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Madelyn and her friend Beth are each baking apple pies and tarts for a bake sale, using the same recipes. Madelyn baked 1 apple pie and 3 apple tarts, using a total of 19 apples. Beth made 10 apple pies and 10 apple tarts, which used 110 apples. How many apples does each dessert require?

An apple pie uses ____ apples and an apple tart requires____apples.

Respuesta :

mhanifa

Answer:

  • An apple pie uses 7 apples and an apple tart requires 4 apples

Step-by-step explanation:

Apple pie - p, apple tart - t

Set the system as follows:

  • p + 3t = 19
  • 10p + 10t  = 110

Solve by substitution, p = 19 - 3t:

  • 10(19 - 3t) + 10t = 110
  • 190 - 30t + 10t = 110
  • 20t = 190 - 110
  • 20t = 80
  • t = 4

Find the value of p:

  • p = 19 - 3*4 = 19 - 12 = 7
  • Apple pie be x
  • Apple tart be y

The equations are

  • x+3y=19--(1)
  • 10x+10y=110=>x+y=11---(2)

Subtracting both equations

[tex]\\ \sf\longmapsto 2y=8[/tex]

[tex]\\ \sf\longmapsto y=4[/tex]

Put in equation (2)

[tex]\\ \sf\longmapsto x+4=11[/tex]

[tex]\\ \sf\longmapsto x=7[/tex]