You can
put this solution on YOUR website!You need to create expressions that describe both the number of bills and the value of those bills.
:
We want to start by defining the variables and since the question is asking how many of each type of bill he has, that gives us a good basis to do this. So:
:
Let o = the number of ones
Let f = the number of fives, and
Let t = the number of tens.
:
One piece of information we have is that he has a total of 95 bills and that he only has ones, fives, and tens. So we can write:
:
Eq 1)
:
Now, the value of the one dollar bills that he has is also o, because each one dollar bill has a value of one dollar. The value of the five dollar bills is 5f, because each five has a value of five dollars, and similarly the value of his ten dollar bills is 10t. Since we know that the total amount of money he has is $575, we can write:
:
Eq 2)
:
So far, so good. Now, twice the number of five dollar bills is 2f, and five more than that is 2f + 5, and we are told that is equal to the number of ones plus the number of tens, o + t. Now we can write:
:
, but we need to rearrange this so that this equation is in the same form as the other two by subtracting 2f from both sides, thus:
:
Eq 3)
:
So now we have three linear equations in three variables. Let's see if there is a solution.
:
Step 1, subtract Eq 3) from Eq 1), term by term:
:
, and simplify
:
Now we know that Daniel has 30 fives and we can substitute this information into Eq 1) and Eq 2), thus:
:
Eq 4)
, which simplifies to
,
:
Eq 5)
, which simplifies to
:
Solving Eq 4) for o, we get
, and then substituting into Eq 5) we get:
:
, then solve for t:
:
:
And now we know that Daniel has 40 tens. Substitute that into Eq 5) to get:
:
:
Giving us the last piece of the puzzle: Daniel has 25 ones.
:
Now we have to check the answer.
:
25 ones plus 30 fives plus 40 tens is, in fact, 95 bills.
$25 in ones, plus $5 times 30 = $150 in fives, plus $10 times 40 = $400 in tens is 25 + 150 + 400 which does, in fact, equal $575. So the answer checks, and perhaps you are a little less confused.
