Question

fifteen darts have landed on the dart board shown. each dart scores 3,5, or 7 points. in how many different ways can the fifteen darts score a total of 75 points

Answer 1

The answer is "8".

Explanation:

Let the number are a, b, c then value is as follows:

a= 3

b= 5

c= 7

The addition of equation ⇒ a+b+c =15....................(i)

multiply by the value ⇒ 3a + 5b + 7c = 75 ...............(ii)

let b= 15-a-c which subtract from equation (ii)

equation:

⇒ 3a + 5b + 7c = 75

⇒ 3a + 5(15-a-c) + 7c = 75

⇒ 3a +75-5a-5c+7c = 75

⇒ 3a -5a-5c+7c = 75-75

⇒ -2a + 2c = 0

⇒ 2(c-a) = 0

⇒ (c-a) = 0

⇒ c=a

if we put value in between 0 to 7 from it satisfies the two equations, with c=a and b = 15 - a - c. So, the correct answer is 8.