Let x be number of $10 dollar bills
Let y be number of $5 dollar bills
Let z be number of $1 dollar bills
From the question, we can come up with three equations (so we can find the values of x, y & z) :
- 10x + 5y + z = 101
- y - x = 5
- z = 4x
The first equation comes from finding the total money Elizabeth has, which is $101.
The second equation comes from value of y (number of $5 bills) is more than value of x (number of $10 bills) by 5 dollars.
The third equation comes from the value of z (number of $1 bills) being 4 times more than the value of x (number of $10 bills).
Now, we will begin to find the value of x, y & z.
From the first equation,
10x + 5y + z = 101
Substitute the third equation (z = 4x) into z:
10x + 5y + 4x = 101
Simplify this and you get,
14x + 5y = 101
Now, we use the second equation. The second equation is y - x = 5. If we try to make y as the subject, it becomes y = 5 + x.
Now, substitute this into the value of y of the last working we did:
14x + 5(5+x) = 101
Simplify that and it becomes:
x = 4
Then, substitute this value of x into the second and third equations to find y and z.
y - x = 5
y - 4 = 5
y = 9
z = 4x
z = 4(4)
z = 16
Finally, let's check these answers by substituting them into the first equation to try and see if the total value is really $101.
10x + 5y + z = 10(4) + 5(9) + 16
10x + 5y + z = 40 + 45 + 16
10x + 5y + z = 101
Thus, our answers are correct. Elizabeth has FOUR $10 bills, NINE $5 bills and SIXTEEN $1 bills.