SOLUTION: how do i solve? The product of 5 and 2 less than triple a number equals the product of 7 and 8 more than twice the number. What is the number? I did this: 5(2)-3n=7(8)+2n

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Question 662785: how do i solve?
The product of 5 and 2 less than triple a number equals the product of 7 and 8 more than twice the number. What is the number?
I did this:
5(2)-3n=7(8)+2n
Found 2 solutions by ewatrrr, DrBeeee:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

The product of 5   and (2 less than triple a number) equals the product of 7   and (8 more than twice the number)

The ands indicate the two terms of the 'product'

   5(3n-2) = 7(2n+8)

   15n-10 = 14n + 56

         n =  66

and...

15%2A66+-+10+=+14%2A66+%2B+56=980

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
You did a no-no.
The first expression should be
(1) 5*(3*n - 2)
The second should be
(2) 7*(8 + 2*n)
See the difference and why?
In the first you have the product of 5 AND (something) or 5 times (something), that (something) is "2 less than 3 times n" or (3*n - 3), giving you
(1) 5*(3*n - 2)
The same applies to the second expression - 7 times "something", which is now (2*n + 8), giving you (2).
The expressions (1) and (2) are equal so we get
(3) 5*(3*n-2) = 7*(2*n+8)
Multiplying (3) out you get
(4) 15*n - 10 = 14*n + 56
Simplify (4) to get
(5) n = 66
Is this correct? Let's check with (3)
Is (5*(3*66-2) = 7*(2*66+8))?
Is (5*(198-2) = 7*(132+8))?
Is (5*196 = 7*140)?
Is (980 = 980)? Yes
Answer: the number is 66.