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.
