Class A folds 160 fewer paper cranes than Class B and 2/3 as many paper cranes as Class C. Class B folds 92 more paper cranes than Class C. How many paper cranes does Class B fold?
Answer (2)
To solve the mathematics problem, we set up a system of equations with the given relations between the number of paper cranes folded by classes A, B, and C. After substituting and simplifying, we find that class B folds 296 paper cranes.
The question is a classic example of a system of equations problem in mathematics. To find out how many paper cranes class B folds, we will define variables for the number of paper cranes each class folds and then set up equations based on the information given. Let's let the variable B represent the number of paper cranes class B folds, A represent class A's count, and C the count for class C.
From the problem, we have the following relations: A = B - 160 (class A folds 160 fewer paper cranes than class B)
A = 2/3 * C (class A folds 2/3 as many paper cranes as class C)
B = C + 92 (class B folds 92 more paper cranes than class C)
Now, because A is the same in the first two equations, we can equate them:
B - 160 = 2/3 * C
Using the third equation, we can substitute for C (C = B - 92) into the equation above:
B - 160 = 2/3 * (B - 92)
Now we solve for B:
B - 160 = 2/3 * B - 2/3 * 92
3 * (B - 160) = 2 * (B - 92)
3B - 480 = 2B - 184
B = 480 - 184
B = 296
Thus, class B folds 296 paper cranes.
Class B folds 296 paper cranes. We determined this by setting up a system of equations based on the relationships given in the problem. After solving the equations, we found the number of paper cranes folded by Class B to be 296.
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