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Tim and Albert had a Chinese and a Mathematics test. Tim’s mark in the Chinese test is twice that of Albert’s. However, Albert got 26 marks more than Tim did in the Mathematics test. After adding, Albert’s sum of the two marks is 121, which is 13 marks less than Tim. What are the four marks of Tim’s and Albert’s tests?Answer: The sum of Tim’s two marks is 121+13=134. Let Tim’s and Albert’s mark in the Mathematics be the same, then Albert’s sum of the two marks would be 121-26=95. Therefore, the difference in their Chinese test mark is 134-95=39. Because the difference in their marks is equal to Albert’s Chinese test mark as Tim’s mark in the test is twice that of Albert’s, ∴ Albert’s Chinese test mark is 39 and Tim’s mark is 39*2=78; Albert’s Mathematics test mark 121-39=82 and Tim’s mark is 134-78=56
Next Question:
Father’s present age is five times the sum of his two sons’ present age. After 6 years, it would shrink to 2 times. Also, 3 years after present, the elder son’s age would be a double of the younger son’s age. How old are the three people?
Answer: Let F be the father’s age, E be the elder son’s age, Y be the younger son’s age: Formula 1: F=5(E+Y) Formula 2: F+6=2(E+6+Y+6) Apply formula 1 into 2: F+6=2(E+6+Y+6) 5(E+Y)+6=2(E+Y)+24 (5-2)(E+Y)=24-6 E+Y=18/3 E+Y=6 ∴F=5*6=30 (Formula 1) Because 3 years after present, the elder son’s age would be a double of the younger son’s age ∴ The elder son’s age is (6+2*3)*2/3-3=5; and the younger son’s age is (6+2*3)*1/3-3=1 ∴ The father’s age is 30, the elder son’s age is 5, the younger son’s age is 1
