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There are two classrooms A and B having a certain number of students. If 5 students are shifted from A to B, then B has twice the number of students as A. If 1 student is sent from B to A, then both classrooms will have the same number of students. How many students are there in B?
22
17
19
26
19
Use the second condition (BтИТ1=A+1) to conclude A=BтИТ2, then substitute directly into the first condition: B+5=2((BтИТ2)тИТ5), which simplifies to B+5=2BтИТ14.
Let A and B be the number of students in classrooms A and B. Two conditions are given: 1) After shifting 5 from A to B, B has twice the students as A. 2) After sending 1 from B to A, both have equal students.
B+5=2(AтИТ5) and BтИТ1=A+1
Use the second condition (BтИТ1=A+1) to conclude A=BтИТ2, then substitute directly into the first condition: B+5=2((BтИТ2)тИТ5), which simplifies to B+5=2BтИТ14.
Students often swap the coefficients in the equation B+5=2(AтИТ5), accidentally writing AтИТ5=2(B+5) instead.
Define Equations
Let A and B be the number of students. Condition 1: B+5=2(AтИТ5). Condition 2: BтИТ1=A+1.
B+5=2AтИТ10, A=BтИТ2
Substitute and Solve
Substitute A=BтИТ2 into the first equation: B+5=2(BтИТ2тИТ5).
B+5=2(BтИТ7)
Final Calculation
Expand the equation: B+5=2BтИТ14. Rearrange to solve for B: B=14+5=19.
B=19
C is correct because the system of linear equations yields B = 19 students in classroom B.
This type of problem is a classic 'Age Problem' variant; always express one variable in terms of the other to reduce the system to a single linear equation.
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