A pound of tin is worth $2 more than a pound of copper. Three pounds of tin are mixed with 7 pounds of copper to make bronze that sells for $3.85 per pound. How much is a pound of tin worth
3 pounds of tin = 3(c+2) dollars
7 pounds of copper = 7 c dollars
10 pounds of bronze = 38.50 dollars
so
7 c + 3 c + 6 = 38.5
c = 3.25 dollars per pound for copper
so
c+2 = 5.25 dollars per pound for tin
cost of pound of copper ---- x
cost of pound of tin -------- x+2
3(x + 2) + 7x = 10(3.85)
3x + 6 + 7x = 38.5
10x = 32.5
x = 3.25
copper sells for $3.25 per pound, and tin sells for $5.25 per pound
To find out how much a pound of tin is worth, we need to break down the information and solve the problem step by step.
Let's start by assigning variables to the unknowns:
Let t be the value of one pound of tin.
And let c be the value of one pound of copper.
We are given that a pound of tin is worth $2 more than a pound of copper, so we can write the equation:
t = c + $2
Next, we are told that three pounds of tin are mixed with seven pounds of copper to make bronze. Therefore, the total weight of the mixture is 3 + 7 = 10 pounds.
The value of the bronze mixture is given to be $3.85 per pound. So, we can write another equation:
(3t + 7c) / 10 = $3.85
Now, we have two equations:
t = c + $2
(3t + 7c) / 10 = $3.85
We can solve these equations simultaneously to find the values of t and c.
Let's start by substituting the first equation into the second equation:
(3(c + $2) + 7c) / 10 = $3.85
Simplifying the equation, we get:
(3c + $6 + 7c) / 10 = $3.85
(10c + $6) / 10 = $3.85
10c + $6 = $38.50
10c = $32.50
Dividing both sides of the equation by 10, we find:
c = $3.25
Now that we know the value of copper, we can substitute this value back into the first equation to get the value of tin:
t = $3.25 + $2
t = $5.25
Therefore, a pound of tin is worth $5.25.