1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Crank
2 years ago
15

Gold used to make jewerly is often a blend of​ gold, silver, and copper. Consider three alloys of these metals. The first alloy

is​ 75% gold,​ 5% silver, and​ 20% copper. The second alloy is​ 75% gold,​ 12.5% silver, and​ 12.5% copper. The third alloy is​ 37.5% gold and​ 62.5% silver. If 100 g of the first alloy costs ​$2500.40​, 100 g of the second alloy costsnbsp $ 2537.75​, and 100 g of the third alloy costs $ 1550.00​, how much does each metal​ cost?
Mathematics
1 answer:
hodyreva [135]2 years ago
3 0

Answer:

Gold - $33, Silver - $5, Copper - $0.02

Step-by-step explanation:

Let $x be the price of one gram of gold, $y - price of 1 g of silver and $z - price of 1 g of copper.

1. The first alloy is​ 75% gold,​ 5% silver, and​ 20% copper, so in 100 g there are 75 g of gold, 5 g of silver and 20 g of copper.  If 100 g of the first alloy costs ​$2500.40​, then

75x+5y+20z=2500.40

2. The second alloy is​ 75% gold,​ 12.5% silver, and​ 12.5% copper, so in 100 g there are 75 g of gold, 12.5 g of silver and 12.5 g of copper.  If 100 g of the first alloy costs ​$2537.75​, then

75x+12.5y+12.5z=2537.75

3. The third alloy is​ 37.5% gold and​ 62.5% silver, so in 100 g there are 37.5 g of gold and 62.5 g of silver .  If 100 g of the first alloy costs ​$1550.00​, then

37.5x+62.5y=1550.00

Solve the system of three equations:

\left\{\begin{array}{l}75x+5y+20z=2500.40\\75x+12.5y+12.5z=2537.75\\37.5x+62.5y=1550.00\end{array}\right.

Find all determinants

\Delta=\|\left[\begin{array}{ccc}75&5&20\\75&12.5&12.5\\37.5&62.5&0\end{array}\right] \|=28125\\ \\\Delta_x=\|\left[\begin{array}{ccc}2500.40&5&20\\2537.75&12.5&12.5\\1550.00&62.5&0\end{array}\right] \|=928125\\ \\\Delta_y=\|\left[\begin{array}{ccc}75&2500.40&20\\75&2537.75&12.5\\37.5&1550&0\end{array}\right] \|=140625\\ \\\Delta_z=\|\left[\begin{array}{ccc}75&5&2500.40\\75&12.5&2537.75\\37.5&62.5&1550\end{array}\right] \|=562.5\\ \\

So,

x=\dfrac{\Delta_x}{\Delta}=\dfrac{928125}{28125}=33\\ \\\\y=\dfrac{\Delta_y}{\Delta}=\dfrac{140625}{28125}=5\\ \\\\z=\dfrac{\Delta_z}{\Delta}=\dfrac{562.5}{28125}=0.02\\ \\

You might be interested in
Which situation shows a constant rate of change.
lana [24]

D because it is the only one that is unpredictable

3 0
3 years ago
Read 2 more answers
Ordered pairs satisfy the equation 3y−9x=9
dalvyx [7]

Answer:

9

Step-by-step explanation:

3 (6)-9 (1)=9

18-9=9

i think that is the answer

6 0
3 years ago
Between what pair of numbers is the product of 289 and 7
Vesna [10]
It's between 2,000 and 3,000. Also 2,020 and 2,030. (The answer is 2,023.) c:
7 0
2 years ago
On a coordinate plane, a circle has a center at point (negative 6, 4).
liraira [26]

Answer:

{x}^{2}  +  {y}^{2}  + 12x - 8y + 4 = 0

7 0
2 years ago
Which of the following expressions represents the verbal description below?
Georgia [21]
  • Cube of the sum of 4 and 9 times x means (4+9x)^3
  • Product of 5times x and the difference of x and 1 means 5x(x-1)

Lets divide

Expression is

\\ \sf\longmapsto \dfrac{(4+9x)^3}{5x(x-1)}

5 0
2 years ago
Read 2 more answers
Other questions:
  • Which is greater 6km or 54,000 mm
    15·2 answers
  • Is 2.9 greater than 2.90
    7·2 answers
  • Which represents the square of the sum of a number and 4 is 36
    13·1 answer
  • How 152 is shown with blocks
    8·2 answers
  • Identify the domain and range of each function.
    9·1 answer
  • Is (2, -3) a solution of the graphed inequality?
    7·1 answer
  • What is the value of 6^3 x 2 3
    11·1 answer
  • PLEASE HELP FAST!!!
    10·1 answer
  • Find the coordinates of the point (x, y)<br> shown on the unit circle.<br> X=
    15·2 answers
  • 12. Un artículo vale 80 dólares después de aplicarle el IVA del 20% ¿Cuánto valdría sin IVA
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!