SOLUTION: The ratio of the price of a cassette to the price of a VCD was 1:5. Each VCD cost $25. On a certain day, the amount of money collected from the sale of both VCDs and cassettes was

Question 1206419: The ratio of the price of a cassette to the price of a VCD was 1:5. Each VCD cost $25. On a certain day, the amount of money collected from the sale of both VCDs and cassettes was $6720. If the number of cassettes sold made up 1/5 of the total number of VCDs and cassettes sold, how many VCDs were sold on that day?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52840) (Show Source): You can put this solution on YOUR website!
.
The ratio of the price of a cassette to the price of a VCD was 1:5. Each VCD cost $25.
On a certain day, the amount of money collected from the sale of both VCDs and cassettes was $6720.
If the number of cassettes sold made up 1/5 of the total number of VCDs and cassettes sold,
how many VCDs were sold on that day?
~~~~~~~~~~~~~~~~~~~~~

Each VCD costs $25. Hence, each cassette costs = 5 dollars. Let x be the number of cassette sold. Then the number of VCD is 4x. The total revenue equation is 5*x + 25*(4x) = 6720 dollars. Simplify and find x 5x + 100x = 6720 105x = 6720 x = 6720/105 = 64. ANSWER. 64 cassettes and 4*64 = 256 VCDs were sold that day.

Solved using one equation in one unknown.

-----------------------

It also can be solved mentally using the grouping method,
without any equations.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
c = number of cassettes
v = number of vcds

ratio of the price of a cassette to the price of a vcd = 1:5.
price of a vcd = 25
price of a cassette = 1/5 * 25 = 5.

you have two equations that need to be solved simultaneously.

they are c + v = yet to be determined
5 * c + 25 * v = 6720

you are given that c = 1/5 * (c + v)
that means that v = 4/5 * (c + v))

in the equation of 5 * c + 25 * v = 6720, replace c with 1/5 * (c + v) and replace v with 4/5 * (c + v) to get:

1/5 * (c + v) * 5 + 4/5 * (c + v) * 25 = 6720

factor out the (c + v) to get:

(c + v) * (1/5 * 5 + 4/5 * 25) = 6720

simplify to get (c + v) * 21 = 6720

solve for (c + v) to get (c + v) = 6720 / 21 = 320.

c = 1/5 * 320 = 64
v = 4/5 * 320 = 256

your total price equation becomes 64 * 5 + 256 * 25 = 6720 which becomes 6720 = 6720 which is true.

your solution is that 256 vcds were sold on that day.

64 cassettes were sold for 64 * 5 = 320
256 vcds were sold for 256 * 25 = 6400
total revenue for the day was 320 + 6400 = 6720.

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