## Sunday, May 6, 2012

### Patrick's 8 questions

Question 1: Find 3 Consecutive numbers such that the sum of the second and three times the first is four more that three times the third.

x + 1 + 3(x) = 3(x + 2) + 4
x + 1 + 3x = 3x + 6 + 4
4x + 1 = 3x + 10
4x - 3x = 10 - 1
x = 9

Question 2: Jim is 4 times as old as Harry, and Harry is 8 years younger than Bill. The sum of the ages of Jim and Harry decreased by Bill's age, is 12. Find their present ages.

4(x - 8) + x - 8 - x = 12
4x - 32 + x - 8 - x = 12
4x + x - x - 32 - 8 = 12
4x - 40 = 12
4x = 12 + 40
4x/4 = 52/4
x = 13

Question 3: The sum of the angles of a triangle is 180 degrees. If the fist angle of a triangle is three times as large as the second, and the third angle is 5 degrees larger than the first, how many degrees are there in each angle ?

3x + x + 3x + 5 = 180
7x + 5 = 180
7x = 180 - 5
7x/7 = 175/7
x = 25

Question 4: The proceeds of a Junior High School dance amounted to \$37.25. If the students paid 35 cents per couple, and non-students paid 50 cents per couple, how many of the 82 couples at the dance were students ?

35x + 50(82 - x) = 3725
35x + 4100 - 50x = 3725
35x - 20x = 3725 - 4100
15x/15 = 375/15
x = 25

Question 5: At what price per kilogram should a merchant sell a mixture of 50 kilograms of nuts if it contains 30 kilograms of almonds worth 40 cents per kilogram, and 20 kilograms of Brazil nuts worth 50 cents per kilogram ?

30(40) + 20(50) = 50x
1200 + 1000 = 50x
2200/50 = 50x/50
44 = x

Question 6: Mr. Jones withdraws \$10 000 from a bank where it was earning 2% interest. He then invests part of the \$10 000 in bonds paying 3%, and the remainder in stocks yielding 4% interest. By investing his \$10 000 in this manner, he increases his yearly income by \$140. How much has he invested in bonds ?

0.03x + 0.04(10 000 - x) = 0.02(10 000) + 140
0.03x + 400 - 0.04x = 200 + 140
0.03x - 0.04x = 340 - 400
- 0.01x/- 0.01 = - 60/- 0.01
x = 6000

Question 7: If pump A and pump B operate together, it takes 12 minutes to empty a swimming pool. By itself, Pump A can empty the pool in 20 minutes. How long would it take to empty the pool of only pump B was working ?

1/20 + 1/R = 1/12
(20)(R)(12)1/20 + (20)(R)(12)1/R = (20)(R)(12)1/12
12R + 240 = 20R
12R - 20R = - 240
- 8R/- 8 = - 240/- 8
R = 30

Question 8: For the Jones family, the trip from home to the cottage and back takes 3 hours. Going to the cottage they travel 50 km/h and coming back they travel 70 km/h. How far away from home is the cottage ?

D1 = D2
ST = ST
50x = 70(3 - x)
50x = 210 - 70x
50x + 70x = 210
120x/120 = 210/120
x = 1.75

D1 = D2
ST = ST
50(1.75) = 70(3 - 1.75)
87.5 = 70(1.25)
87.5 = 87.5