Unit 3: 5-2 HW Question 8, 5.2.17 HW Score: \( 87.5 \%, 7 \) of 8 points Points: 0 of 1 If \( \$ 1 \) in U.S. dollars is equivalent to 6.42 Chinese yuan, convert \( \$ 14,000 \) to yuan. Use proportions to solve the problem. \( \$ 14,000 \) in U.S. dollars is equivalent to \( \square \) yuan

Sure, I'd be happy to help you convert \$14,000 to Chinese yuan using proportions! **Given:** - Exchange rate: \$1 = ¥6.42 - Amount to convert: \$14,000 **Step-by-Step Solution:** 1. **Set Up the Proportion:** You can set up the proportion based on the given exchange rate: \[ \frac{\$1}{¥6.42} = \frac{\$14,\!000}{¥x} \] Here, \( x \) represents the amount in yuan that you're trying to find. 2. **Solve for \( x \):** To find \( x \), cross-multiply and solve the equation: \[ \$1 \times ¥x = \$14,\!000 \times ¥6.42 \] \[ ¥x = \$14,\!000 \times 6.42 \] \[ ¥x = 14,\!000 \times 6.42 \] 3. **Calculate the Conversion:** Multiply 14,000 by 6.42: \[ 14,\!000 \times 6 = 84,\!000 \] \[ 14,\!000 \times 0.42 = 5,\!880 \] \[ 84,\!000 + 5,\!880 = 89,\!880 \] 4. **Final Answer:** \[ \$14,\!000 = ¥89,\!880 \] **So, \$14,000 in U.S. dollars is equivalent to ¥89,880 Chinese yuan.**