MHB Can you solve this problem using bar models and ratios?

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The discussion focuses on solving a problem involving ratios and bar models related to counters in three boxes. It outlines the relationships between the quantities of counters in boxes A, B, and C using equations derived from given ratios. The ratios are specified as 5:3 for boxes A and B, and 2:1 for boxes B and C. Additionally, it describes the changes in the number of counters after some are removed and moved between the boxes, leading to an equal count in each box. The thread emphasizes the importance of showing effort in problem-solving by writing relevant equations.
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I need help with how to use bar models with these kinda stuff. Thanks
 
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This is not pre-uni topics, but i'd just like to know the answer thanks! 😊
 
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.
 
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.
 
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