A city’s school board merged the city’s two rival high schools to form

Question

A city’s school board merged the city’s two rival high schools to form one new high school, which then had 4500 students. 10% of the students at high school A and 15% of students at high school B were in the marching band. If all marching band members joined the new school’s marching band, which then had 570 members, how many students did school A have before the merge?

A. 2100
B. 2200
C. 2300
D. 2400
E. 2500

A. 2100
B. 2200
C. 2300
D. 2400
E. 2500

giobas · Answer

lets say total number of school a is x and total number of school b is y

x + y = 4500
0.1x + 0.15y = 570

to equations 2 variables, if we solve

x =2100 and y = 2400

answer is A

0akshay0 · Answer

A + B = 4500 (total number of students of both schools) 0.1A + 0.15B =570 (10% of the students at high school A and 15% of students at high school B were in the marching band which consisted of 570 students) On solving the above 2 equations, we have A = 2100 and B = 2400 Hence Option A is correct Hit Kudos if you liked it 8-)

Jayeshvekariya · Answer

A+B=4500
A=x
B=4500-X
0.1x + 0.15(4500-X)=570
Solving this equation gives x=2100
So correct Ans is A.

Sent from my MotoG3 using  GMAT Club Forum mobile app

Diwakar003 · Answer

One of those sums in which solving via options is quicker. Thanks to the answer being in the first option.

A+B=4500,

Option A) A=2100, so B=2400. 10%A=210, 15%B=360. Total members of band => 210+360=570. Hence the answer.

Cheers!

ScottTargetTestPrep · Answer

We can let A = the number of students from school A, and B = the number of students from school B. Since the combined schools had 4,500 students, we know that A + B = 4,500.

We are also given that 10% of the students at high school A and 15% of the students at high school B were in the marching band, which has 570 members. Thus:

0.1A + 0.15B = 570

10A + 15B = 57,000

We can isolate B in the first equation and we have: B = 4,500 - A.

We now can substitute 4,500 - A for B in the equation 10A + 15B = 57,000:

10A + 15(4,500 - A) = 57,000

10A + 67,500 - 15A = 57,000

-5A = -10,500

A = 2,100

Answer: A

HimanshuW11 · Answer

With this weighted average problem, there are two core methods you could use to solve it: algebraically, or with the weighted average mapping strategy. For this problem, the algebra requires a bit less creativity to set up. You're looking at:

a+b=4500
and 
0.1a+0.15b=570
If you multiply the second equation by −10, that allows you to use the Elimination Method to get rid of the variable a
−10(0.1a+0.15b=570)
 means that: 
−a+−1.5b=−5700
Stack that up with the other equation and add:

a+b=4500
−a+−1.5b=−5700
And you have one equation, all with the variable b
−0.5b=−1200, so multiply by −2 to arrive at:
b=2400
That means that a, the variable in question, must be 2100
2100, making answer choice A correct.

poorvi125 · Answer

Nice question  Bunuel

May also tag this as a Mixture Problem.

A city’s school board merged the city’s two rival high schools to form

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