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29 Nov 2024, 01:30
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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.
A. $1,200 less
B. $500 less
C. $300 less
D. $300 more
E. The costs are equal.
29 Nov 2024, 02:54
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University A
tuition fees annually - $9000
Room and Boarding price annually - $3000
Total fee for University A = $12000
University B
Tuition fees annually - x
Room and Boarding price annually - y
Tuition fee of A is 10% less than that of B
x - 10% of x = $9000
0.9x = $9000
x = $10000
Boarding price of A is 20% more than B
y + 20% of y = $3000
1.2y = $3000
y = $2500
Total fee for University B = $12500
Total fee of A is less than that of B by = $12500 - $12000 = $500 annually (OPTION B)
Concept to focus on:
If p is 10% more than q, then q is not 10% less than p.
tuition fees annually - $9000
Room and Boarding price annually - $3000
Total fee for University A = $12000
University B
Tuition fees annually - x
Room and Boarding price annually - y
Tuition fee of A is 10% less than that of B
x - 10% of x = $9000
0.9x = $9000
x = $10000
Boarding price of A is 20% more than B
y + 20% of y = $3000
1.2y = $3000
y = $2500
Total fee for University B = $12500
Total fee of A is less than that of B by = $12500 - $12000 = $500 annually (OPTION B)
Concept to focus on:
If p is 10% more than q, then q is not 10% less than p.
Bunuel
29 Nov 2024, 10:46
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Let's say Uni B tuition is Bt and room is Br
University A charges 10% less than University B does for tuition
\(\\
Bt*\frac{90}{100}=9000\\
Bt= 10,000\\
\)
20% more than University B does for room and board
\(\\
Br*\frac{120}{100}=3000\\
Br=2500\\
\)
The total annual cost of tuition, room and board is how much more or less at University A than it is at University B?
Total for Uni A= \(9000+3000=12000\)
Total for Uni B= \(10,000+2500=12500\)
So, at Uni A it is 500 less than Uni B.
Option B.
Hope it helps.
University A charges 10% less than University B does for tuition
\(\\
Bt*\frac{90}{100}=9000\\
Bt= 10,000\\
\)
20% more than University B does for room and board
\(\\
Br*\frac{120}{100}=3000\\
Br=2500\\
\)
The total annual cost of tuition, room and board is how much more or less at University A than it is at University B?
Total for Uni A= \(9000+3000=12000\)
Total for Uni B= \(10,000+2500=12500\)
So, at Uni A it is 500 less than Uni B.
Option B.
Hope it helps.
