The sports master explained to the headmaster that 3 baseballs and 1 cricket ball
weighed the same as 14 tennis balls. He also found that 1 baseball and 6 tennis balls
exactly balanced 1 cricket ball. ‘That is interesting,’ said the headmaster, ‘and how
many tennis balls weigh the same as 1 cricket ball?’ he asked. What was the
sports master's answer?
3b+c = 14t
b+6t = 1c
so, find c in terms of t:
c = 14t-3b = 14t-3(c-6t)
c = 14t-3c+18t
4c = 32t
c = 8t
To find the sports master's answer, let's analyze the given information step by step.
First, we are given that 3 baseballs and 1 cricket ball weigh the same as 14 tennis balls. Let's denote the weight of a baseball as "b," the weight of a cricket ball as "c," and the weight of a tennis ball as "t." Therefore, we have the equation:
3b + 1c = 14t Equation 1
Next, it is mentioned that 1 baseball and 6 tennis balls exactly balance 1 cricket ball. We can represent this information as:
1b + 6t = 1c Equation 2
Now, the headmaster asks how many tennis balls weigh the same as 1 cricket ball. We need to solve for the number of tennis balls (t) in terms of cricket ball (c). To do this, we can rearrange Equation 2:
6t = 1c - 1b [(subtracting b from both sides]
t = (1c - 1b)/6 [(dividing by 6 on both sides]
So, for each cricket ball, we need to divide the difference between one cricket ball (c) and one baseball (b) by 6 to get the weight equivalent in tennis balls.
Based on the given information, the sports master's answer would be: For each cricket ball, it would weigh (1c - 1b)/6 tennis balls.