You must so acceptance to 2 classmates. A solicit for clarification on the arrangement used, a impulse for an totter arrangement of solving the amount or a open criticise about the technique would all be expend. I'm enduring that a "thank you" for an exceptionally obvious sense would so be welcome!
bank teller has 54 $5 and $20 bills in her specie drawer. The estimate of the bills is $780. How manifold $5 bills are there?
Let x correspondent the calculate of $5 bills
Let y correspondent the calculate of $20 bills
We perceive that conjointly the calculate of $5 bills and the $20 bills is 54, so that is the foremost equation.
x + y = 54
Next the completion estimate of the bills fully is $780, that is the assist equation.
5x + 20y = 780
Now that we bear our two equations we can explain by superabundance. To do so we bear to re-establish our foremost equation solving for one of the waverings
x + y = 54
- x - x
y = 54 - x
Next we accomplish represent this equation into the assist, and explain.
5x + 20(54 - x) = 780 (extend 20 and 54, and extend 20 and - x)
5x + 1080 – 20x = 780 (cohere 5x and – 20x)
-15x + 1080 = 780 (remove 1080 from twain policys)
-15x = -300 (part-among by -15)
x = 20
Now that we bear our x estimate, we can explain for y using our foremost equation.
20 + y = 54 (remove 20 from each policy)
y = 34
Finally, to bridle the acceptances you represent them into twain of the equations.
20 + 34 = 54
54 = 54 TRUE
5(20) + 20(34) = 780
100 + 680 = 780
780 = 780 TRUE
The terminal acceptance is there are 20 - $5 bills, and 34 - $20 bills.
What would your acceptance be to this peculiar?
The Problem: (x) calculate of bracelets are sold at $8 each and (y) calculate of necklaces at $11 each. Rosaria compensated a completion of $1140. How manifold bracelets and how manifold necklaces did she escheatment?
The Solution:
1.) Listed are the perceiven factors:
o Let the calculate of bracelets be represented by the wavering: x
⦁ In which each x calculate of bracelets are priced at $8
o Let the calculate of necklaces be represented by the wavering: y
⦁ In which each y calculate of necklaces are priced at $11
2.) Listed are the relationships betwixt x and y
o x + y = 120
o $8x + $11y = $1140
3.) I accomplish be using twain exportation and superabundance arrangement to explain this amount
.
⦁ First I'd use the exportation arrangement to explain the scheme of equations:
o -8[x + y = 120] -8x – 8y = -(960) (extend equation by -8)
8x + 11y = 1140 (segregate x- wavering)
o $8x + $11y = $1140 3y = 180 (separate y through resistance)
3 3
y = 60 (solve)
⦁ Second I'd use the superabundance arrangement to explain for the x-variable:
o x + y = 120 x + (60) = 120 (represent perceiven wavering: y)
x = 60 (sickly removeion to separate x)
o $8x + $11y = $1140 x = 60 (solve)
Checking the acceptances:
o x + y = 120 (60) + (60) = 120 (represent perceiven waverings)
8(60) + 11(60) = 1140 (Solve)
o $8x + $11y = $1140
SOLUTION: Rosaria escheatmentd 60 bracelets and 60 necklaces.
what accomplish be your acceptance to this peculiar?