Question 1137567: A book seller buys 120 volumes of a certain books.He sells some for 18p each and disposes of the remainder during a sale at 12p each.If the total receipts are £
19.20.how many volumes were sold at each price
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Let x = # of the 18 p volumes, y = # of 12 p volumes.
From the condition, you have these 2 equations
x + y = 120 (1) (counting volumes)
18*x + 12*y = 1920 (2) (counting money, in " p ")
From equation (1), express y = 120 - x and substitute it into equation (2), You will get
18x + 12*(120-x) = 1920.
Express x and calculate answer
x =  = 80.
Then from equation (1), y = 120 - 80 = 40.
ANSWER. 80 volumes at 18p and 40 volumes at 12p.
CHECK. 80*18 + 40*12 = 1920 p. ! Correct !
The problem solved using 2-equation setup and the Substitution method.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! i believe 100 pence to the pound.
x = number of books sold at 18 pence each.
y = number of books sold at 12 pence each.
total books sold is 120, therefore x + y = 120.
since 100 pence to the pound, then 19.20 pounds is equal to 1920 pence.
total receipts were 1920 pence, therefore 18x + 12y = 1920
you have 2 equations that need to be solved simultaneously.
they are:
x + y = 120
18x + 12y = 1920
in the first equation, solve for y to get y = 120 - x.
in the second equation, replace y with 120 - x to get 18x + 12 * (120 - x) = 1920.
simplify to get 18x + 1440 - 12x = 1920.
combine like terms and subtract 1440 from both sides of the equation to get 6x = 1920 - 1440
combine like terms to get 6x = 480.
solve for x to get x = 80.
since x = 80, then y = 140 - x = 40.
total receipts are (18 * 80) + (12 * 40) = (800 + 640) + (400 + 80) = 1440 + 580 = 1920.
total receipts for books at 18 pence each is 1440 pence = 14.40 pounds.
total receipts for books at 12 pence each is 580 pence = 5.80 pounds.
total receipts is 1920 pence = 19.20 pounds.
your solution is that 80 books were sold at 18 pence each and 40 books were sold at 12 pence each.
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