A merchandise vendor at a sports arena is given a large uncounted pile of hats and shirts to sell at a game. Hats cost $17.00 each, and shirts sell for $21.00 each. At the end of the night, the vendor realized he forgot to keep track of how many quantities of each item he sold. However, he does know that he sold 75 total items and sold $1,435.00 of merchandise. How many hats did he sell? Number of hats =

Given : A merchandise vendor at a sports arena is given a large uncounted pile of hats and shirts to sell at a game. Hats cost $17.00 each, and shirts sell for $21.00 each. At the end of the night, the vendor realized he forgot to keep track of how many quantities of each item he sold. However, he does know that he sold 75 total items and sold $1,435.00 of merchandise.

To find : How many hats did he sell?

Solution :

Let the number hats sold be 'x'.

Let the number of shirts sold be 'y'.

The vendor sold a total of 75 items,

i.e. [tex]x+y= 75[/tex] ....(1)

Hats cost $17.00 each, and shirts sell for $21.00 each.

Since he sold a total of $1,435 of merchandise,

i.e. [tex]17x+21y= 1435[/tex] .....(2)

Solving equation (1) and (2),

Substitute the value of x from (1) and put into (2),

[tex]17(75-y)+21y= 1435[/tex]

[tex]1275-17y+21y= 1435[/tex]

[tex]4y= 1435-1275[/tex]

[tex]4y=160[/tex]

[tex]y=\frac{160}{4}[/tex]

[tex]y=40[/tex]

Substitute in equation (1),

[tex]x+40= 75[/tex]

[tex]x=75-40[/tex]

[tex]x=35[/tex]

So, She sold 35 hats and 40 shirts.

Therefore, The number of hats sell is 35.