Question 158201
let a = number of small paintings sold
let b = number of large paintings sold
let $60*a = amount of money received from the sale of small paintings
let $180*b = amount of money received from the sale of large paintings
number of total paintings sold is 12, so
first equation becomes: a+b=12
total amount of money made is $1200, so
second equation becomes: $60*a + $180*b = $1200.
to solve this equation, you need to remove one of the unknowns by describing it in terms of the other unknown.
in the first equation, if a+b=12, then a=12-b (subtract b from both sides of the equation).
in the second equation substitute (12-b) everywhere you see a.
second equation becomes
$60*(12-b) + $180*b = $1200
expanding this becomes
$60*12 - $60*b + $180*b = $1200
multiplying out all factors that can be multiplied, this becomes
$720 - $60*b + $180*b = $1200
subtracting $720 from both sides of the equation and it becomes
$180*b - $60*b = $1200 - $720
adding like terms together, this becomes
$120*b = $480
solving for b, this equation becomes
b=$480/$120 = 4
if b = 4, then 12-b = 8 = a
a = 8
b = 4
second equation becomes
$60*8 + $180*4 = $1200, which becomes
$480 + $720 = $1200, which becomes
$1200 = $1200 proving the formula is correct with
a = 8, and
b = 4