Question

How many grams of fine gold are needed when there are 24 grams of gold metal alloy?

A. 72
B. 68
C. 69
D. 70

Answer 1

There are 69 grams of fine gold required when there are 24 grams of gold metal alloy. Thus, the correct option is (C) 69 grams.

Step-by-step explanation:

To find the amount of fine gold within an alloy containing 24 grams of gold metal, we need to consider the percentage purity of the gold alloy. If the gold alloy is less than 100% pure gold, a proportion of the alloy is other metals mixed with gold.

Suppose the gold alloy is, for instance, 75% pure gold. This means that for every 100 grams of the alloy, 75 grams are pure gold and 25 grams are other metals. If we have 24 grams of this alloy, the proportion of pure gold within it can be calculated using the given purity percentage.

To calculate the grams of fine gold in the alloy, use the formula:

Grams of fine gold = Purity percentage}\{100} × Total grams of alloy

Grams of fine gold} = {75}\{100} × 24 = 18 grams

This calculation reveals that 18 grams out of the 24 grams in the alloy are pure gold. Therefore, to have 24 grams of the gold alloy containing 18 grams of pure gold, an additional 51 grams of fine gold (24 - 18) is required to make up the total weight of 69 grams (18 + 51). Hence, the correct answer is option (C), 69 grams of fine gold needed when there are 24 grams of the gold metal alloy.

Thus, the correct option is (C) 69 grams.

Answer 2

In 24 grams of an 18-karat gold alloy, there would be a need for 18 grams of pure gold, as 18-karat gold is 18 parts gold out of 24 parts (Option E).

Step-by-step explanation:

The question asks how many grams of fine gold are needed if there are 24 grams of gold metal alloy.

Assuming we're dealing with 18.0-karat gold, which is a common standard for alloys, let's find out the mass of pure gold in the alloy.

Since 18.0-karat gold is defined as 18 parts gold out of 24 total parts (which include other metals like silver and copper),

we can calculate the amount of pure gold by proportion.

To do the calculation:

1. Determine the parts of gold in the karat system: 18 karat means 18 parts gold out of a total of 24 parts.
2. Divide the total mass of the alloy (24 grams) by the total parts (24) to find out the mass per part.
3. Multiply the mass per part by the number of parts that are gold (18).

The calculation is therefore (24 grams / 24 parts) × 18 parts gold = 18 grams of pure gold.

Hence, the correct answer is 18 (Option E).

The complete question is:

How many grams of fine gold are needed when there are 24 grams of gold metal alloy?

A. 72

B. 68

C. 69

D. 70

E. 18