Darren bought some paint. he used 2 1/4 gallons painting his living room. after that, he had 3 5/6 gallons left. how much paint did he buy?

Step-by-step explanation:

We can make the conversion from mixed numbers to improper fractions:

Then:

We need to add the fractions in order to calculate the amount of paint Darren bought. Since the denominators are differente, we must find the Least Common Denominator (LCD):

Then:

To convert this improper fraction to a mixed number:

Then:

Step-by-step explanation:

Let's pretend this was just whole numbers.  So used 2 gallons and had 3 left.  Hopefully it's clear you'd have started with 5.  It's basically an algebra equation.  If we say x is the starting amount then

x-2 = 3

x = 5.  Let me know if that doesn't make sense.  Now though we can plug in the actual values.

x - 2 1/4 = 3 5/6

x = 2 1/4 + 3 5/6

x = 5 1/4 + 5/6

Now, to add fractions you need to change the denominator.  You need to know you can change fractions by multiplying the numerator and denominator by a number.  so 1/2 can be 2/4 because 1*2 = 2 and 2*2 = 4.  So on you can make it 3/6, 4/8 and on and on and on.  This is what we want to use.

We have 1/4 and 5/6.  Well, you could try increasing both one by one until you get the same denominator, but a way to do it in one step is to multiply one by the other's denominator.  so 1/4 = (1*6)/(4*6) = 6/24 and similarly 5/6 = (5*4)/(6*4) = 20/24.  So now we are adding 6/24 + 20/24 = 26/24 or 1 2/24 = 1 1/12.  ANyway, now you are adding

5 1/4 + 5/6 = 5 + 1 1/12 = 6 1/12.  There is a different way to add fractions, but it's a little more involved and this way always works so that's what I use.  

y-1700=200(x+4)

step-by-step explanation:

200(x+4) is 200x + 800 she is saving 200 per week x is the weeks and the -1700 is. us that’s howmuch she already had