星期四, 4月 21, 2011

44.The sum of 3 consecutive EVEN number is 90. Find the smallest one.

Let x be the smallest consecutive EVEN number.
x + (x + 2) + (x + 4) = 90
=> 3x + 6 = 90
=> x + 2 = 30
=> x = 28

45.The sum of two numbers is 84 . If the large number exceed 3 times the smaller by 4 ,what is the larger number?

Let x be the smaller number and y be the larger number.
x + y = 84 --- (1)
3x + 4 = y --- (2)

Put (2) into (1):
x + (3x + 4) = 84
4x + 4 = 84
x = 20 --- (3)

Put (3) back into (2):
3(20) + 4 = y
y = 64

i.e. The larger number is 64.

46. Betty is 5kg lighter than twice the weight of Jane. Their total weight is 94kg. Find the weight of Betty.

Let x be the weight of Betty and y be the weight of Jane.
x + y = 94 --(1)
x + 5 = 2y --(2)

(1)-(2):
x + y - x - 5 = 94 - 2y
y - 5 = 94 - 2y
3y = 99
y = 33 --(3)

Put (3) back into (1):
x + 33 = 94
x = 61

i.e. the weight of Betty is 61 kg

47. There are some \$2 coins and some \$5 coins. The total value is \$78 and the total number of coins is 21 . Find the number of \$5 coins.

Let b be number of \$2 coins and e be number of \$5 coins.
2b + 5e = 78 --(1)
b + e = 21 --(2)

(1) - 2 x (2):
2b + 5e - 2b - 2e = 78 - 2 x 21
3e = 36
e = 12

i.e. the number of \$5 coins is 12.

48. There are some \$2 coins and some \$5 coins. The total value is \$169 and the total number of coins is 50 . Find the number of \$2 coins

Let b be number of \$2 coins and e be number of \$5 coins.
2b + 5e = 169 --(1)
b + e = 50 --(2)

(1)- 5 x (2):
2b + 5e - 5b - 5e = 169 - 250
81 = 3b
b = 27

i.e. the number of \$2 coins is 27