a jeweler purchased 5 oz of a gold alloy and 20 oz of a silver alloy for a total cost of $540. The next day at the same price per ounce, the jeweler purchased 4 oz of th egold alloy and 25 oz of the silver alloy for a total cost of $450. Find the cost per ounce of the gold and silver alloys.

cost of gold per ounce = x

cost of silver per ounce = y

5x + 20y = 540 ---> x + 4y = 108
4x + 25y = 450

1st equation times 4
4x + 16y = 432
4x + 25y = 450
subtract them
9y = 18
y = 2
sub into x+4y = 108
x + 8 = 108
x = 100

WOW! $100 per ounce of gold
Quickly tell me where and I will be a millionaire within a few hours, lol

To find the cost per ounce of the gold and silver alloys, we can set up a system of equations.

Let's denote the cost per ounce of the gold alloy as "x" and the cost per ounce of the silver alloy as "y".

From the given information, we know that:

5x + 20y = 540 (equation 1) - representing the cost of the alloys purchased on the first day.
4x + 25y = 450 (equation 2) - representing the cost of the alloys purchased on the second day.

Now, we have a system of two equations and two unknowns. We can solve this system using any method of solving simultaneous equations. Here, we will use the substitution method to find the values of x and y.

From equation 1, we can solve for x in terms of y:
5x = 540 - 20y
x = (540 - 20y) / 5
x = 108 - 4y (equation 3)

Now, substitute the value of x from equation 3 into equation 2:
4(108 - 4y) + 25y = 450

Simplify and solve for y:
432 - 16y + 25y = 450
432 + 9y = 450
9y = 450 - 432
9y = 18
y = 18 / 9
y = 2

Now that we have the value of y, we can substitute it back into equation 3 to find x:
x = 108 - 4(2)
x = 108 - 8
x = 100

Therefore, the cost per ounce of the gold alloy is $100 and the cost per ounce of the silver alloy is $2.