\#6 i MODELING REAL LIFE A gold alloy contains 15 milligrams of gold for every 4 milligrams of copper. A jeweler uses 48 milligrams of copper to make the alloy. How much gold does the jeweler use to make the alloy?

Question

UpStudy AI · Accepted Answer

To determine how much gold the jeweler uses to make the alloy, we can use the given ratio of gold to copper and set up a proportion.

**Given:**
- The ratio of gold to copper is 15 milligrams (mg) of gold for every 4 mg of copper.
- The jeweler uses 48 mg of copper.

**Steps to Solve:**

1. **Set Up the Proportion:**
   
   $$
   \frac{\text{Gold}}{\text{Copper}} = \frac{15 \text{ mg}}{4 \text{ mg}} = \frac{x \text{ mg}}{48 \text{ mg}}
   $$
   
   Here, $$ x $$ represents the amount of gold needed.

2. **Solve for $$ x $$:**
   
   $$
   \frac{15}{4} = \frac{x}{48}
   $$
   
   Cross-multiply to solve for $$ x $$:
   
   $$
   4x = 15 \times 48
   $$
   
   $$
   4x = 720
   $$
   
   $$
   x = \frac{720}{4} = 180 \text{ mg}
   $$

**Conclusion:**
The jeweler uses **180 milligrams of gold** to make the alloy with 48 milligrams of copper.
The jeweler uses 180 milligrams of gold to make the alloy.

\#6 i MODELING REAL LIFE A gold alloy contains 15 milligrams of gold for every 4 milligrams of copper. A jeweler uses 48 milligrams of copper to make the alloy. How much gold does the jeweler use to make the alloy?

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