Write an equation for: melissa has 6 times as many quarters as michelle. together they have 896 quarters. how many quarters, q, does michelle have? and .

Okay, so in this equation we will use the following variables:

a: for the number of quarters Michelle has
b: for the number of quarters Melissa has
q: for total number of quarters

So first, we will write out the statement "Melissa has 6 times as many quarters as Michelle" in the form of an equation:

6 times the number of quarters Michelle has is equal to the number of quarters Melissa has, or:
6(a)=b

So, we now know that Melissa has  6 times as many quarters as Michelle. 

So, if the have 896 quarters total, then you can write the problem as the number of quarters Michelle has added to the number of quarters Melissa has. This can be expressed as:

a+b=q

Since we know that Melissa has 6 times the quarters as Michelle, 6a is equivalent to b:

(6×a)=b

Since we know the total number of quarters is 896, we can rewrite it as this:

a+(6×a)= 896

Now that we know this, we can solve the problem with the following steps:

6a+a=7a

7a=896

896÷7= 128

a= 128

So, now that we know that know that Michelle has 128 quarters, we can find out how many Melissa has:

128×6= 768

Melissa has 768 quarters.

Now we check our work:

128+ (6×128)= 768

If everything is correct the following should be true:

a=128

and 

b=768

So, Michelle has 128 quarters.