British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 320 grams of a copper-silver alloy that is 20% copper by weight? (Round your answers to one decimal place.)
copper: what is 20 percent of 320
silver: what is 80 percent of 320
This is hardly algebra.
To solve this problem, we can set up a system of equations based on the information provided. Let's define two variables:
Let x be the amount of pure copper (in grams) used to prepare the alloy.
Let y be the amount of British sterling silver (in grams) used to prepare the alloy.
From the given information, we know that British sterling silver is a copper-silver alloy that is 7.5% copper by weight. This means that in 100 grams of British sterling silver, there are 7.5 grams of copper. Therefore, in y grams of British sterling silver, the amount of copper is (7.5/100) * y = 0.075y grams.
We are also given that the resulting copper-silver alloy should be 20% copper by weight. This means that in 320 grams of the alloy, the amount of copper is (20/100) * 320 = 64 grams.
Now we can set up the equations:
Equation 1: x + 0.075y = 64 (representing the total amount of copper in the alloy)
Equation 2: x + y = 320 (representing the total weight of the alloy)
We can use these equations to solve for x and y.
First, let's solve equation 2 for x: x = 320 - y.
Now substitute this into equation 1:
320 - y + 0.075y = 64
320 - 0.925y = 64
-0.925y = -256
y ≈ 277.3 grams
Substituting this back into equation 2:
x + 277.3 = 320
x ≈ 42.7 grams
Therefore, to prepare 320 grams of a copper-silver alloy that is 20% copper by weight, you should use approximately 42.7 grams of pure copper and 277.3 grams of British sterling silver.