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What is the value of y in 3/5(y/8+1/4)=9/16?

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2 Answers

The trick to this problem is finding the lowest common denominator so that you can work the problem algebraically.  First, we should distribute the 3/5 through the parentheses, just as if it weren't a fraction at all.  Just be sure you're multiplying all the parts correctly, and you'll get:
 
3y/40 + 3/20 = 9/16
 
Now for the lowest common denominator, or LCD.  In this case it's helpful to break each denominator down into its smallest factors, then compare the three sets and see what we need to add to each one to make them all the same:
 
40                                  20                             16
4 * 10                           2 * 10                         4 * 4
2 * 2 * 2 * 5                 2 * 2 * 5                     2 * 2 * 2 * 2
 
So clearly the lowest common denominator would be 2 * 2 * 2 * 2 * 5, or 80.  Go ahead and multiply the first term by 2/2, the second term by 4/4, and the third term by 5/5 to get them all to be over 80.
 
NOTE:  We can do this because 2/2, 4/4, and 5/5 are all just fancy ways of writing "1", so we're essentially multiplying each term by 1, which will keep it the same value.  This is just a way of writing the same number in a different form so that it's easier to work with.
 
So we'll have:
 
6y/80 + 12/80 = 45/80
 
Now, at any point from here on, we could multiply each term by 80 and get rid of the fractions completely. I'm going to go two more steps before I do that, though, just to be sure I'm not missing anything.
 
6y/80 = 45/80 - 12/80                  Subtract the 12/80 from both sides.
 
6y/80 = 33/80                             Do the subtraction on the right to combine terms.
 
Now I'll get rid of the fractions:
 
6y = 33                                      Multiply both sides by 80.
 
y = 33/6                                     Divide both sides by 6.
 
Now, 33 is not divisible by 6, but they're both divisible by 3, so let's simplify as much as we can:
 
y = 11/2, or 5.5, or 5 1/2, depending on what format you and your teacher prefer.  I prefer 11/2.
 
If you plug 11/2 back into the original problem, you do in fact end up with 9/16 = 9/16.
 
Hope this helped!  Let me know if you still have questions!