Question 1168690
x = number of pens sold separately.
y = number of pens sold in sets of 5.
when the pens are sold separately, they cost 8.90 each.
when the pens are sold in sets of 5, they cost 44.50 plus the buyer gets a pen for free.
your cost equation is 8.90 * x + 44.50 * y = 1174.80.
8.90 is the cost for one pen sold separately.
44.50 is the cost of a set of 5 pens with 1 extra pen given for free.
you are given that 2/3 of the pens were sold in sets of 5.
since (x + y) is the total number of pens sold, this means that y = 2/3 * (x + y)
simplify to get y = 2/3 * x + 2/3 * y
subtract 2/3 * y from both sides of this equation to get:
y - 2/3 * y = 2/3 * x
combine like terms to get:
1/3 * y = 2/3 * x
solve for y to get:
y = 3/1 * 2/3 * x
simplify to get:
y = 2 * x
in the equation of 8.90 * x + 44.50 * y = 1174.80, replace y with 2 * x to get:
8.90 * x + 44.50 * 2 * x = 1174.80.
simplify to get:
8.90 * x + 89 * x = 1174.80
combine like terms to get:
97.90 * x = 1174.80
solve for x to get:
x = 12.
since y = 2 * x, then you get:
y = 24.
your equation of 8.90 * x + 44.50 * y = 1174.80 becomes:
8.90 * 12 + 44.50 * 24 = 1174.80 which becomes 1174.80 = 1174.80, confirming the values of x and y are good.
x represents 1 pen.
y represents 6 pens (5 that are bought and 1 that is given free).
12 * 1 + 24 * 6 = 156.
there must have been 156 pens in the box.
that's your solution, as best i can determine.
he sold 12 pens separately.
he sold 24 sets of 5 pens each = 120 pens
he gave away 24 pens (1 for each set of 5).
the total pens in the box had to be 12 + 120 + 24 = 156.
132 of the pens were sold.
24 were given away.