I know I have the equations right, I have reread the question and I can't write the equations any other way.
Beth has $218 in $10, $5 and $1 bills. There are forty-six bills in all and four more fives than tens. How many bill of each kind are there?
For my first equation: 10x + 5y + 1z = 218
Second equation: x + y + z = 46
The third equation: y=4x
I used y=4x and entered it into the first and second equation and came up with.
First equation: 10x + 5(4x) + z = 218 and got 30x + z =218
Second equation: x + 4x + z = 46 resulting in 5x + z =46.
I thought I would solve for x by eliminating the variable z. So I multiplied the second equation by -1. Giving me -5x-z=-46. Thus setting up to solve for x.
30x+z=218
-5x -z = 46
--------------
25x=172
Divided both sides by 25 and got 6.88. I didn't think that I could get this kind of answer and be right. I tried rounding up to 7 and continuing to solve for y and z, but when I checked my work it didn't add up right. Where did I go wrong?
Beth has $218 in $10, $5 and $1 bills. There are forty-six bills in all and four more fives than tens. How many bill of each kind are there?
For my first equation: 10x + 5y + 1z = 218
Second equation: x + y + z = 46
The third equation: y=4x
I used y=4x and entered it into the first and second equation and came up with.
First equation: 10x + 5(4x) + z = 218 and got 30x + z =218
Second equation: x + 4x + z = 46 resulting in 5x + z =46.
I thought I would solve for x by eliminating the variable z. So I multiplied the second equation by -1. Giving me -5x-z=-46. Thus setting up to solve for x.
30x+z=218
-5x -z = 46
--------------
25x=172
Divided both sides by 25 and got 6.88. I didn't think that I could get this kind of answer and be right. I tried rounding up to 7 and continuing to solve for y and z, but when I checked my work it didn't add up right. Where did I go wrong?