Fill in the blanks-
1). the sum of two consecutive odd numbers is 84, the number are ________ and________
2). A number multiplied by 6 and then reduced by 3 gives 69, the number is_______
3). The number of boys is 3/2 the number of girls in class. the total strength is 40. the number of girls is ______
To find the missing values, we can use algebraic equations. Let's go through each question step by step:
1) The sum of two consecutive odd numbers is 84. Let's denote the smaller odd number as "x" and the next consecutive odd number as "x + 2". The equation representing the sum would be:
x + (x + 2) = 84
Simplifying the equation:
2x + 2 = 84
2x = 82
x = 41
So the smaller odd number is 41, and the next consecutive odd number is 41 + 2 = 43.
The numbers are 41 and 43.
2) A number multiplied by 6 and then reduced by 3 gives 69. Let's represent the unknown number as "x". The equation would be:
6x - 3 = 69
Adding 3 to both sides:
6x = 72
x = 12
So the number is 12.
3) The number of boys is 3/2 the number of girls in the class. The total strength is 40. Let's represent the number of girls as "x". The equation would be:
(3/2)x + x = 40
Combining like terms:
(5/2)x = 40
Now, to isolate "x", we can multiply both sides by the reciprocal of (5/2), which is (2/5):
(5/2)x * (2/5) = 40 * (2/5)
x = 16
So the number of girls is 16.
1. It must be in the 40s to be consecutive. Explore for yourself.
2. Reverse the process. Add 3 to 69, then divide by 6.
3. Let x = # girls, then 2/3x = # boys.
x + 2/3x = 40, assuming that strength = number of children.