Answer:
x = 48 and y = 104
Step-by-step explanation:
Given equations are:
[tex]x+y = 152\\8.5x+12y=1656[/tex]
From equation 1:
[tex]x = 152-y[/tex]
Putting the value of y in equation 2
[tex]8.5(152-y)+12y = 1656\\1292-8.5y+12y = 1656\\3.5y+1292 = 1656\\3.5y = 1656-1292\\3.5y = 364\\\frac{3.5y}{3.5} = \frac{364}{3.5}\\y = 104[/tex]
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
[tex]x+y = 152\\x+ 104 = 152\\x = 152-104\\x = 48[/tex]
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.
