- #1
SDAlgebra
- 5
- 0
Can you solve this problem using bar models and ratios?
In summary, the conversation discusses a problem involving three boxes with counters and the ratio between them. The task is to find the values of a, b, c, and x using four equations. The ratios of counters between the boxes are given as 5:3 for A to B and 2:1 for B to C. Some counters are removed from box A and 54 counters are moved from box B to box C, resulting in the same number of counters in each box. The four equations are 3a=5b, b=2c, a-x=b-54, and b-54=c+54.
- #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
- 2,436
- 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.
1. What are bar models with ratios used for?
Bar models with ratios are used to visually represent the relationship between different quantities or values. They are commonly used in math to solve problems involving ratios, proportions, and percentages.
2. How do you create a bar model with ratios?
To create a bar model with ratios, first identify the quantities or values involved and determine the ratio between them. Then, draw a bar representing the total amount and divide it into segments according to the ratio. Finally, label each segment with the corresponding quantity or value.
3. Can bar models with ratios be used for any type of problem?
Bar models with ratios are most commonly used for math problems involving ratios, proportions, and percentages. However, they can also be used for other types of problems that involve comparing quantities or values.
4. How can bar models with ratios help with problem solving?
Bar models with ratios can help with problem solving by providing a visual representation of the relationship between different quantities or values. This can make it easier to understand and solve the problem, especially for visual learners.
5. Are there any limitations to using bar models with ratios?
While bar models with ratios can be a helpful tool for problem solving, they may not be suitable for every problem. Some problems may be more complex and require different methods of solving. Additionally, bar models with ratios may not be as effective for individuals who are not visual learners.
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