SOLUTIONS TO MATHEMATICS WORKSHEET 2

Here are the solutions for the Mathematics Worksheet 2 (Problems).

1. 80% A = 50% (20% C) is just the same as 0.8 A = 0.5 (0.2 C). Simplifying the right side of the equation, it will be 0.8 A = 0.1 C. Divide both sides by 0.8, A= 1/8 C or C/8 (d).


2. Let x be the first integer. The sum of the first 5 of 10 consecutive integers: x + (x+1) + (x +2) + (x + 3) + (x + 4) =  265. Simplifying the left side of the equation, 5x + 10 = 265. Transpose 10 to the right side, it will be 5x = 255. Then, we get the sum of the last five integers which is (x +5) + (x + 6) + (x + 7) + (x + 8) + (x+ 9). Simplifying it will be 5x + 35. We substitute the value of 5x we got from the sum of the first 5 integers which is 255 to get the sum of the last 5 integers that is 5x + 35 = 255 + 35 = 290 (a).


3. Anna can do the typing job in 10 hours which means in 1 hour, she can finish 1/10 of the job. After she has worked for 2 hours, she already finished 2/10 or 1/5 of the job when Chester came to help her. So, 4/5 of the job is remaining for the two of them to finish the job. Let's say Chester can finish the job alone in x hours which means in 1 hour, he can finish 1/x of the job. In 3 hours, Anna can finish 3/10 [3 * 1/10] of the remaining job while Chester can do it 3/x [3* 1/x]. We put it in equation: 3/10 + 3/x = 4/5. Transpose 3/10 to the right, it will be 3/x = 4/5 - 3/10. Simplifying the right side, 3/x = 5/10. Cross multiply: 30 = 5x. Therefore, x = 6 (a).


4. 50 liters of 3% salt solution (97% water) minus X liters of 100% pure water = (50-X) liters of 5% salt solution (95% water). We put that in equation form: 50 (0.97)  - X = 0.95 (50-X). Simplifying both sides, we have 48.5 - X = 47.5 - 0.95 X. Segregating the X's and the constants, we have 1 = 0.05 X. Therefore X = 20 (d).


5. a = 3c + 1 and b = 2c -1. If c = 4, then a = 13 and b = 7. 2a = 26 and 3c = 21. We subtract 3c from 2a, we get 26 - 21 = 5 (d).


6. The equation to this problem is: (600/x) - [ 600/ (x + 3)] = 10. TO get rid of the denominators, let's multiply both sides by x (x +3). We will get 600(x+3) - 600x = 10x(x+3). Simplifying, we get 10 (x^2) + 30x - 1800 = 0. This is a quadratic equation. To solve this we use the method of factoring. Using trial and error, the factors we get are (x+15) (x-12) = 0. The answers are 12 and -15. We choose the positive number so the final answer is 12 (b).


7. In hour, 1/6 of the tank will be filled in water and 1/9 of it will be emptied. So, we subtract 1/9 from 1/6. And the answer is 1/18 which means 1/18 of the tank will be filled in water. So, it takes 18 hours for the tank to be full (c).


8. The speed is x/50. The formula is speed = distance/time. Time = distance/speed. So, time = 10/ (x/50). Simplifying, the time will be 500/x (a).


9. Let's say Michael is x years old now and Peter is 3x. Five years ago, Michael's age is x-5 while Peter's age is 3x-5. The equation will be 4 (x-5) = 3x-5. Simplifying the left side of the equation, it will be 4x - 20 = 3x - 5. Segregating the x's and the constants, it will be x = 15. So, Michael's age is 15 (c).


10. [a- (b-c)] - [(a-b)-c] = (a-b+c) - (a-b-c) = a - b + c - a + b + c = 2c  (c).