University A charges $9,000 annually for tuition and $3,000 annually for room and board. University A charges 10% less

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University A charges $9,000 annually for tuition and $3,000 annually for room and board. University A charges 10% less than University B does for tuition and 20% more than University B does for room and board. The total annual cost of tuition, room and board is how much more or less at University A than it is at University B?

A. $1,200 less
B. $500 less
C. $300 less
D. $300 more
E. The costs are equal.


OA B

Source: Princeton Review

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BTGmoderatorDC wrote:
Wed Sep 01, 2021 7:49 pm
University A charges $9,000 annually for tuition and $3,000 annually for room and board. University A charges 10% less than University B does for tuition and 20% more than University B does for room and board. The total annual cost of tuition, room and board is how much more or less at University A than it is at University B?

A. $1,200 less
B. $500 less
C. $300 less
D. $300 more
E. The costs are equal.


OA B

Source: Princeton Review
Let's try as follows:

\(90\%\) of B's tuition fees \(= 9000\$\)

\(\Rightarrow\) B's tuition fees \(= \dfrac{9000}{90} \ast 100 = 10,000\$\)

\(120\%\) of B's room and board fees \(= 3000\$\)

\(\Rightarrow\) B's room and board fees \(= \dfrac{3000}{120} \ast 100 = 2500\$\)

University A

Tuition fees \(= 9000\$\)

Room and board \(= 3000\$\)

Total fees of University A \(= 9000\$ + 3000\$ = 12,000\$\)

University B

B's tuition fees \(= 10,000\$\)

B's room and board fees \(= 2500\$\)

Total fees of University B \(= 10,000\$+2,500\$ = 12,500\$\)

Therefore

Difference \(= 12,500 - 12,000 =500\$ \Longrightarrow \) B