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...

 

Answer by DrBeeee(684)   (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. 

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