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Sondra is making 10 quarts of punch from fruit juice and club soda. The quarts of fruit juice equal 4 times the quarts of club soda. How many quarts of each does she need?
A8 quarts of fruit juice and 2 quarts of club soda
B2 quarts of fruit juice and 8 quarts of club soda
C6 quarts of fruit juice and 4 quarts of club soda
D5 quarts of fruit juice and 5 quarts of club soda
Answer & Solution
Correct answer: A. 8 quarts of fruit juice and 2 quarts of club soda
1. Let f be the quarts of fruit juice and c be the quarts of club soda, giving the system f + c = 10 and f = 4c.
2. Substitute 4c for f in the first equation: 4c plus c equals 10, so 5c equals 10.
3. Divide by 5 to get c equals 2, then substitute back: f equals 4 times 2, which is 8.
4. Sondra needs 8 quarts of fruit juice and 2 quarts of club soda, and checking confirms 8 is 4 times 2, and 8 plus 2 equals 10.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.1 Solve Systems of Equations by Graphing_
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