MHB Arithmetic problem: What is the capacity of each Breaker"?

Click For Summary
The problem involves finding the capacity of beakers containing oil and water, given that there are 6 beakers of oil and 12 of water, totaling 66 liters. The equation derived from the scenario is 6O + 12W = 66, which simplifies to O + 2W = 11. This equation allows for multiple solutions, even when restricted to positive integers. Examples of possible capacities include (1,5), (3,4), (5,3), (7,2), and (9,1). The discussion highlights the need for additional constraints to determine a unique solution.
Penguin1
Messages
1
Reaction score
0
Need help with this
I have 6 beaker of oil and 12 breaker of water, the total amount combined are 66 litres .
What is the capacity of each Breaker"?
 
Mathematics news on Phys.org
Without more information, we will get an infinite number of ordered pairs that will satisfy the problem. I am assuming that the beakers containing oil all have the same capacity, and the beakers containing water all have the same capacity...and if we let $O$ be the capacity of the beakers containing oil, and $W$ be the capacity of the beakers containing water, we may state:

$$6O+12W=66$$

Divide through by 6:

$$O+2W=11$$

Even if we restrict ourselves to the positive integers, we have numerous solutions:

$$(O,W)=(1,5),\,(3,4),\,(5,3),\,(7,2),\,(9,1)$$
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
Replies
28
Views
851
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
651
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K