Official Solution:
Substance X constitutes 0.8 percent of the weight of Solution A and 1.8 percent of the weight of Solution B. When 300 grams of Solution A are combined with 700 grams of Solution B, what percentage of the weight does Substance X represent in the resulting mixture?
A. 1.5%
B. 1.9%
C. 10%
D. 15%
E. 19%
Algebraic solution:
Substance X constitutes 0.8 percent of the weight of Solution A and 1.8 percent of the weight of Solution B. Thus, 300 grams of Solution A contains 0.8% of 300 grams (0.008*300 = 2.4 grams) of Substance X, while 700 grams of Solution B contains 1.8% of 700 grams (0.018*700 = 12.6 grams) of Substance X. When the two solutions are combined, the resulting mixture weighs 1000 grams and contains 2.4 + 12.6 = 15 grams of Substance X. This means that Substance X represents 1.5% of the weight of the resulting solution (15/1000*100 = 1.5%).
Shortcut solution:
Substance X constitutes 0.8 percent of the weight of Solution A and 1.8 percent of the weight of Solution B. The percentage of Substance X in the resulting mixture (Solution A + Solution B) must lie between 0.8 percent and 1.8 percent. Only 1.5% fits within this range.
Answer: A