SOLUTION: A factory baked some cakes. 70% of the cakes were sold at full price and 3/4 of the remainder were sold at a discount of 40%. The remaining 33 cakes were spoilt and had to be throw

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A factory baked some cakes. 70% of the cakes were sold at full price and 3/4 of the remainder were sold at a discount of 40%. The remaining 33 cakes were spoilt and had to be throw      Log On


   

Question 1203156: A factory baked some cakes. 70% of the cakes were sold at full price and 3/4 of the remainder were sold at a discount of 40%. The remaining 33 cakes were spoilt and had to be thrown away. The factory collected $17635.20 from the sales of the cakes. What was the full price of a cake?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.
A factory baked some cakes.
70% of the cakes were sold at full price and
3/4 of the remainder were sold at a discount of 40%.
The remaining 33 cakes were spoilt and had to be thrown away.
The factory collected $17635.20 from the sales of the cakes.
What was the full price of a cake?
~~~~~~~~~~~~~~~ 

Let x = the full price (now an unknown value).

Let n be the number of cakes baked.


Then we have these two equations for n and x

    0.7n + 0.75*(n-0.7n) + 33 = n               (1)  (total baked cakes)

    0.7n*x + 0.75*(n-0.7n)*0.6x = 17635.20.     (2)  (total money collected)


From equation (1)

    0.7n + 0.75*0.3n + 33 = n,

    (0.7+0.75*0.3)n + 33 = n

     0.925n + 33 = n

     33 = n - 0.925n

     33 = 0.075n

     n  = 33/0.075 = 440.


So, the number of cakes baked was 440.


Now equation (2) takes the form

    0.7*440x + 0.75*0.3*440*0.6*x = 17635.20

    (0.7*440 + 0.75*0.3*440*0.6)x = 17635.20

     367.4x                       = 17635.20

          x                       = 17635.20/367.4 = 48.


ANSWER.  The full price of a cake was 48 monetary units.

Solved.



Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
A factory baked some cakes. 70% of the cakes were sold at full price and 3/4 of the remainder were sold at a discount of 40%. The remaining 33 cakes were spoilt and had to be thrown away. The factory collected $17635.20 from the sales of the cakes. What was the full price of a cake?

Let number of cakes baked be C
After 70% were sold at full price, 30% of C, or .3C remained
After ¾ of remainder were sold at a discount, ¼ of remainder, or ¼(.3C), or .3C%2F4 remained
Since 33 cakes remained in the end, then matrix%281%2C3%2C+.3C%2F4%2C+%22=%22%2C+33%29
                                          .3C = 4(33) ----- Cross-multiplying 
                 Number of cakes baked, or 
 
With number of cakes baked being 440, and 70%, or 308 (.7 * 440) being sold at full price (P), 
proceeds from sale at full price = 308P

With ¾ of remainder, or ¾(440 - 308) = ¾(132) = 3(33) = 99 being sold at a 40% discount (price of .6P),
proceeds from selling 99 at a 40% discount = 99(.6P) = 59.4P 

With proceeds from all sales being 17,635.2, we get: 308P + 59.4P = 17,635.2
                                                           367.4P = 17,635.2
                                      Full price of a cake, or