Question

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.

Answer 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

`\\ \tt\hookrightarrow 4h+8m=12\dots(3)`

Subtract (3) and (2)

`\\ \tt\hookrightarrow 3m=3`

`\\ \tt\hookrightarrow m=1`

Put in eq(1)

`\\ \tt\hookrightarrow h+2=3`

`\\ \tt\hookrightarrow h=1`

Answer 2

• Both the hat and mask cost $1

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