Nadia and Siti each had some money. The ratio of Nadia's money to Siti's money was 7 : 4. After Nadia spent $21 and Siti saved an extra $9, they had the same amount of money. How much money did Nadia have at first?
Show Worked Solution
Worked Solution
Step 1: Set up the ratio using a variable.
Let Nadia's money = 7k and Siti's money = 4k.
Step 2: Write the equation using the equal-amount condition.
After Nadia spends $21: Nadia has 7k − 21.
After Siti saves $9: Siti has 4k + 9.
They are equal: 7k − 21 = 4k + 9
Step 3: Solve for k.
7k − 4k = 9 + 21
3k = 30
k = 10
Step 4: Find Nadia's original amount.
Nadia = 7k = 7 × 10 = $70
Step 5: Verify.
Nadia: $70 − $21 = $49. Siti: $40 + $9 = $49. Equal. ✓
Answer: $70
Correct answer: $70
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