Question 158201This question is from textbook Intermediate Algebra for College Students
: Painting Sales: Joseph DeGuizman, an artist, sells both large paintings and small paintings. He sells his small paintings for $60 and his large paintings for $180. At the end of the week he determined that the total amount he made selling 12 paintings was $1200. Determine the number of small and the number of large paintings that he sold.
---I know the answers, more importantly, I cant understand how to setup the equation(s) to get the answers.
This question is from textbook Intermediate Algebra for College Students
Found 2 solutions by checkley77, gonzo:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! S+L=12 OR S=12-L
60S+180L=1,200
SUBSTITUTING (12-L) FOR S IN THE SECOND EQUATION WE GET:
60(12-L)+180L=1,200
720-60L+180L=1,200
120L=1,200-720
120L=480
L=480/120
L=4 LARGE PAINTING SOLD.
S=4=12
S=12-4
S=8 SMALL PAINTINGS SOLD.
PROOF:
60*8+4*180=1,200
480+720=1,200
1,200=1,200
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! 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
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