- #1
SDAlgebra
- 5
- 0
Can you solve this problem using bar models and ratios?
Click For Summary
Discussion Overview
The discussion revolves around solving a problem involving ratios and bar models, specifically focusing on the relationships between the quantities of counters in three boxes. Participants explore how to set up equations based on given ratios and conditions related to the movement of counters.
Discussion Character
- Homework-related
- Mathematical reasoning
Main Points Raised
- One participant requests assistance with using bar models for the problem.
- Another participant notes that the problem is appropriate for middle or high school level and suggests that the thread starter should demonstrate some effort in solving it.
- A participant defines variables for the counters in each box and establishes equations based on the provided ratios: a/5 = b/3 and b/2 = c/1.
- The same participant outlines the conditions after counters are removed and moved, leading to a system of four equations to solve for the unknowns a, b, c, and x.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the approach to solving the problem, as there is a mix of requests for help and suggestions for how to engage with the problem more actively.
Contextual Notes
Some participants emphasize the need for the thread starter to clarify their understanding of the problem and show their work, indicating that the discussion may depend on the definitions and interpretations of the ratios and conditions provided.
- #2
SDAlgebra
- 5
- 0
This is not pre-uni topics, but i'd just like to know the answer thanks! 
- #3
Evgeny.Makarov
Gold Member
MHB
- 2,434
- 4
This is, in fact, a middle or high school-level problem. https://mathhelpboards.com/help/forum_rules/ ask thread starters to show some effort. In this case this may mean writing equations describing the relationship between the quantities of counters in the three boxes or describing what you do and don't understand about this problem.
- #4
HOI
- 921
- 2
Let a be the number of counters in box A, b the number of counters in box B, and c the number of counters in box C.
"The ratio of counters in box A to box B is 5:3."
so a/5= b/3 and 3a= 5b
"The ratio of counters in box B to box C is 2:1."
so b/2= c/1 and b= 2c.
"Some counters are removed from box A."
Call the number of counters removed x. Now there are a- x counters in box A.
"54 counters are moved from box B to box C."
Now there are b- 54 counters in box B and c+ 54 counters in box C.
"There are now the same number of counters in each box."
a- x= b- 54 and b- 54= c+ 54.
We have four equations
3a= 5b
b= 2c
a- x= b- 54 and
b- 54= c+ 54
to solve for a, b, c, and x.
"The ratio of counters in box A to box B is 5:3."
so a/5= b/3 and 3a= 5b
"The ratio of counters in box B to box C is 2:1."
so b/2= c/1 and b= 2c.
"Some counters are removed from box A."
Call the number of counters removed x. Now there are a- x counters in box A.
"54 counters are moved from box B to box C."
Now there are b- 54 counters in box B and c+ 54 counters in box C.
"There are now the same number of counters in each box."
a- x= b- 54 and b- 54= c+ 54.
We have four equations
3a= 5b
b= 2c
a- x= b- 54 and
b- 54= c+ 54
to solve for a, b, c, and x.
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