SOLUTION: The ratio of cassettes to compact discs was 10 to 3, and the number of cassettes was 10 less than 5 time the number of compact discs. How many cassettes were there?

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Question 64504This question is from textbook An Incremental DEvelopment
: The ratio of cassettes to compact discs was 10 to 3, and the number of cassettes was 10 less than 5 time the number of compact discs. How many cassettes were there?
This question is from textbook An Incremental DEvelopment

Found 2 solutions by ankor@dixie-net.com, ptaylor:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The ratio of cassettes to compact discs was 10 to 3, and the number of cassettes was 10 less than 5 time the number of compact discs. How many cassettes were there?
:
Let the number of cassettes be 10x, then the number of discs will be 3x
:
10x = 5(3x) - 10
10x = 15x - 10
10x - 15x = - 10
-5x = -10
x = -10/-5
x = 2
:
20 cassettes; 6 discs
:
Check: 20 = 5(6) - 10

Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=number of compact discs
Then 5 times the number of CD's=5x and 10 less than 5 times the number of CDs is 5x-10
Therefore the number of cassettes is 5x-10
Now we are told that the ratio of cassettes to CDs which is((5x-10)/x)equals 10/3 so our equation to solve is:
(5x-10)/x=10/3 multiply both sides by 3x to get rid of the fractions and we get:
3(5x-10)=10x or
15x-30=10x subtracting 10x from both sides and adding 30 to both sides we have:
15x-10x=30
5x=30
x=6 the number of CDs
5x-10=(5)(6)-10=30-10=20 number of cassettes
ck
((5)(6)-10)/6=10/3
(30-10)/6=10/3
20/6=10/3
10/3=10/3
Hope this helps. Happy holidays.---ptaylor