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A shop sells party hats and masks. On a particular morning, 10 hats and 20 masks were sold for $30. In the afternoon, 8 hats and 10 masks were sold for $18. Find the cost of each hat and each mask.

Respuesta :

mhanifa

Answer:

  • Both the hat and mask cost $1

Step-by-step explanation:

Let the cost of each hat is x and each mask is y.

According to the question, set the equations:

  • 10x + 20y = 30
  • 8x + 10y = 18

Double the second equation and subtract the first one:

  • 8x*2 + 10y*2 - 10x - 20y = 18*2 - 30
  • 16x - 10x = 36 - 30
  • 6x = 6
  • x = 1

Find the value of y:

  • 10*1 + 20y = 30
  • 20y = 30 - 10
  • 20y = 20
  • y = 1
  • hats be h and masks be m

Equations are

  • 10h+20m=30=>h+2m=3--(1)
  • 8h+10y=18=>4h+5m=9--(2)

Eq(1)×4

[tex]\\ \tt\hookrightarrow 4h+8m=12\dots(3)[/tex]

Subtract (3) and (2)

[tex]\\ \tt\hookrightarrow 3m=3[/tex]

[tex]\\ \tt\hookrightarrow m=1[/tex]

Put in eq(1)

[tex]\\ \tt\hookrightarrow h+2=3[/tex]

[tex]\\ \tt\hookrightarrow h=1[/tex]

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