An archer’s score is calculated by the formula, where b is the number

Question

An archer’s score is calculated by the formula \(\frac{50b-10a}{10+s}\), where b is the number of bull’s-eyes hit, a is the total number of arrows shot, and s is the time in seconds it took the archer to shoot. By how many points would an archer who took 10 seconds to shoot 10 arrows and hit all bull’s-eyes beat an archer who shot twice as many arrows and hit half as many bull’s-eyes in 15 seconds?

(A) 2
(B) 7
(C) 10
(D) 18
(E) 20

(A) 2
(B) 7
(C) 10
(D) 18
(E) 20

chetan2u · Answer

\frac{50b-10a}{10+s} ,

1) a=b=10 and s=10
So first archer gets 
 \frac{50*10-10*10}{10+10}=(500-100)/20=20 ,

2) a=20, b=5 and s=15
 \frac{50*5-10*20}{10+15}=50/25=2 ,

Difference=20-2=18

D

contenteditor · Answer

Hi Bunuel.

Thanks for the solution. But I am not clear about one thing, how do you understand that the value of b is 10 because it is not clearly mentioned in the problem. it's written in the problem " Hit all bull’s-eyes beat an archer " so how do I know the specific value of b.

Thanks

kunal2110 · Answer

Here the question says he shot 10 arrows and all hit bull's eye hence a=10 and b=10

Sand1995 · Answer

I am not clear about one thing, how do you understand that the value of b is 10 because it is not clearly mentioned in the problem. it's written in the problem " Hit all bull’s-eyes beat an archer " so how do I know the specific value of b.

masakiyada · Answer

I had the same issue regarding the variable b, the number of bull’s-eye hit. So I actually left b as it is, and went ahead and set up the equation.

(50*2b-10*10)/(10+10) – (50b-10*20)/(10+15)
=(100b-100)/20 – (50b-200)/25
=5b-5-(2b-8)
=5b-5-2b+8
=3b+3
=3(b+1) → so now, we know that the difference is a multiple of 3. I glanced at the answer choices, and found the only one choice that is a multiple of 3. →18 (D)

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An archer’s score is calculated by the formula, where b is the number

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An archer’s score is calculated by the formula, where b is the number

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