Help Us Solve This Equation: 2/3 k - (k + 1/4) = 1/12 (k + 4)

[amandablackwood]

Hey guys - It's me again. Listen, I need help once more.

My husband and I have both tried to solve this equation, and still can't match it to the answer book. Can anyone out there explain how we can put the answer back into the problem and it doesn't work out for us? What step are we missing here?

2/3 k - (k + 1/4) = 1/12 (k + 4)

40/60 k - (k + 15/60) = 5/60 (k + 240/60)

Eventually we solved :

k = -7/5, as the answer book said we should.

When we put k = -7/5 back into the equation, it didnt work. Let me show you...

2/3 (-7/5) - (-7/5 + 1/4) = 1/12 (-7/5 + 4)

40/60 k (-84/60) - (-84/60 + 15/60) = 5/60 (-84/60 + 240/60)

-3360/60 - (-69/60) = 5/60 (324/60)

-3429/60 = 1620/60

?

It doesn't work!

Anyone know what we've collectively missed over here? Thanks a bunch, guys. I appreciate all the help! I could really use an explanation of how these things work, if anyone is so inclined to help! It would help us greatly in future problems! Thanks...

 

[jamesrc]

-3360/60 - (-69/60) = 5/60 (324/60)

Two mistakes in this line:

$$\frac{40}{60}\cdot\frac{-84}{60} = -\frac{3360}{3600} = -\frac{56}{60}$$

so, you lost a factor of 60 in the denominator.

Secondly, you added wrong on the right hand side: -84+240 = 156, not 324.

Just be more careful and you'll do fine.

 

[amandablackwood]

The answer book (Checking Your Solution) gives the final result as 13/60 = 13/60. Any idea how they came up with that? They don't show the work and we can't see the right path to take!

Also, what rule did it take to figure 3360/3600? We're missing that one, I'm afraid...


Thanks a bunch!

 

[jamesrc]

Once you have substituted in your value for k and simplify both sides, you should end up with 13/60=13/60. So the short answer is, you're already on the right path, you just need to fix up those two errors and finish it up.

For the 3360/3600 part:

you started with (40/60)*(-84/60)

When multiplying fractions, it's usually a good idea to factor first and then reduce, but anyway:
- if you multiply the numerators, 40*-84= -3360
- it you multply the denominators, 60*60 = 3600, so the fraction becomes -3360/3600 (which can be simplified to -56/60 assuming you want to keep a common denominator of 60 for the rest of the problem)