math

You must also respond to 2 classmates. A request for clarification on the procedure used, a suggestion for an alternate method of solving the problem or a general comment about the technique would all be appropriate. I’m sure that a “thank you” for an exceptionally clear explanation would also be welcome!
bank teller has 54 $5 and $20 bills in her cash drawer. The value of the bills is $780. How many $5 bills are there?
Let x equal the number of $5 bills
Let y equal the number of $20 bills
We know that together the number of $5 bills and the $20 bills is 54, so that is the first equation.
x + y = 54
Next the total value of the bills combined is $780, that is the second equation.
5x + 20y = 780
Now that we have our two equations we can solve by substitution. To do so we have to rearrange our first equation solving for one of the variables
x + y = 54
– x – x
y = 54 – x
Next we will substitute this equation into the second, and solve.
5x + 20(54 – x) = 780 (multiply 20 and 54, and multiply 20 and – x)
5x + 1080 – 20x = 780 (combine 5x and – 20x)
-15x + 1080 = 780 (subtract 1080 from both sides)
-15x = -300 (divide by -15) 
x = 20 
Now that we have our x value, we can solve for y using our first equation.
20 + y = 54 (subtract 20 from each side)
y = 34
Finally, to check the answers you substitute them into both of the equations.
20 + 34 = 54
54 = 54 TRUE
5(20) + 20(34) = 780
100 + 680 = 780
780 = 780 TRUE
The final answer is there are 20 – $5 bills, and 34 – $20 bills.
What would your response be to this person?
The Problem: (x) number of bracelets are sold at $8 each and (y) number of necklaces at $11 each. Rosaria paid a total of $1140. How many bracelets and how many necklaces did she purchase?
The Solution:
1.) Listed are the known factors:
o Let the number of bracelets be represented by the variable: x
⦁ In which each x number of bracelets are priced at $8
o Let the number of necklaces be represented by the variable: y
⦁ In which each y number of necklaces are priced at $11
2.) Listed are the relationships between x and y 
o x + y = 120
o $8x + $11y = $1140
3.) I will be using both elimination and substitution process to solve this problem
.
⦁ First I’d use the elimination process to solve the system of equations: 
o -8[x + y = 120] -8x – 8y = -(960) (multiply equation by -8)
8x + 11y = 1140 (eliminate x- variable)
o $8x + $11y = $1140 3y = 180 (isolate y through division)
3 3
y = 60 (solve)
⦁ Second I’d use the substitution process to solve for the x-variable:
o x + y = 120 x + (60) = 120 (substitute known variable: y)
x = 60 (simple subtraction to isolate x)
o $8x + $11y = $1140 x = 60 (solve)
Checking the answers:
o x + y = 120 (60) + (60) = 120 (substitute known variables)
8(60) + 11(60) = 1140 (Solve)
o $8x + $11y = $1140
SOLUTION: Rosaria purchased 60 bracelets and 60 necklaces. 
what will be your response to this person?