Gold weighs 19.3 grams per cubic centimeter (cc), and silver weighs 10.5 grams per cc.
A. Write a formula for the weight of one cc of a mizture of silver and gold in terms of the volume of gold in the cc.
B. If one cc of mizture weighs 12.7 grams, what is the weight of gold in it?
A. To write a formula for the weight of one cc of a mixture of silver and gold in terms of the volume of gold in the cc, we need to consider the weights of gold and silver separately.
Let:
- V_gold be the volume of gold in the cc (in cubic centimeters).
- V_silver be the volume of silver in the cc (in cubic centimeters).
- W_gold be the weight of gold in the cc (in grams).
- W_silver be the weight of silver in the cc (in grams).
Given the densities:
- Gold weighs 19.3 grams per cc.
- Silver weighs 10.5 grams per cc.
Since density is defined as weight/volume, we can express the weights of gold and silver in terms of their respective volumes using the given densities:
- W_gold = V_gold * 19.3 grams/cc
- W_silver = V_silver * 10.5 grams/cc
The total weight of the mixture is the sum of the weights of gold and silver:
- Total weight = W_gold + W_silver
Since the total weight is given as 12.7 grams, we have the equation:
- W_gold + W_silver = 12.7 grams
B. To find the weight of gold in the mixture when one cc of the mixture weighs 12.7 grams, we substitute the given information into the equation derived in part A:
- W_gold + W_silver = 12.7 grams
Substituting the expressions for W_gold and W_silver using the given densities:
- V_gold * 19.3 grams/cc + V_silver * 10.5 grams/cc = 12.7 grams
Since we want to find the weight of gold, we set V_silver to 0, as there is no silver present in the mixture:
- V_gold * 19.3 grams/cc + 0 * 10.5 grams/cc = 12.7 grams
- V_gold * 19.3 grams/cc = 12.7 grams
Now, solve the equation for V_gold:
- V_gold = 12.7 grams / 19.3 grams/cc
Substitute the value for V_gold back into the expression for W_gold to find the weight of gold:
- W_gold = V_gold * 19.3 grams/cc
Compute the value of W_gold using the calculated value of V_gold, and that would be the weight of gold in the mixture.