Question

X + y = 152,

8.5x + 12y = 1,656

How many hats were sold?

Answer 1

48 hats

Explanation:

Answer 2

x = 48 and y = 104

Explanation:

Given equations are:

`x+y = 152\\8.5x+12y=1656`

From equation 1:

`x = 152-y`

Putting the value of y in equation 2

`8.5(152-y)+12y = 1656\\1292-8.5y+12y = 1656\\3.5y+1292 = 1656\\3.5y = 1656-1292\\3.5y = 364\\(3.5y)/(3.5) = (364)/(3.5)\\y = 104`

Now we have to put the value of y in one of the equation to find the value of x

Putting y = 104 in the first equation

`x+y = 152\\x+ 104 = 152\\x = 152-104\\x = 48`

Hence,

The solution of the system of equations is x = 48 and y = 104

The value of variable which was assumed for number of hats, is the total number of hats.