Model and Reason with Equations and Inequalities: Part One — Test
Question 6 • Algebra II
Meryl needs to add enough water to 11 gallons of an 18 percent detergent solution to make a 12 percent detergent solution. Which equation can she use to find g , the number of gallons of water she should add? Original (Gallons) Added (Gallons) New (Gallons) Amount of Detergent 1 point 9 8 0 Amount of Solution 11 g
Answer
A
the fraction with numerator 11 plus g and denominator 1 point 9 8 is equal to 12 over 100
B
the fraction with numerator 1 point 9 8 and denominator 11 plus g minus 12 over 100 is equal to 1
C
the fraction with numerator 1 point 9 8 and denominator 11 plus g plus 12 over 100 is equal to 1
D
the fraction with numerator 1 point 9 8 and denominator 11 plus g is equal to 12 over 100
Explanation
The original solution contains 11 × 0.18 = 1.98 gallons of detergent. Adding water does not change the amount of detergent, so the new solution has 1.98 gallons of detergent and 11 + g gallons total. For a 12% solution, the detergent-to-solution ratio must be 1.98/(11 + g) = 12/100, which is choice D.
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