The number of three-point baskets from the substitution method is 15.
According to the statement
we have given that the total score of basket ball is 105 points and there were as many two-point baskets as free throws (1 point each), and the number of three-point baskets was five less than the number of free throws.
And we have to find the number of three-point baskets.
So, For this purpose, we know that the
Final Score S = 105
Two point baskets T = Free throws F -(1)
Three point baskets H = F - 5 -(2)
Now, we know that the
The final score is equal to 3 times the number of three point baskets plus 2 times the number of two point baskets plus 1 times the number of free throws
So,
S = (3*H) + (2*T) + (1*F)
Here we can use substitution method,
Now we can substitute
105 = 3H + 2T + 1F
105 = 3H + 2F + 1F {substitute from equation (1)}
105 = 3(F-5} + 2F + 1F {substitute from equation (2)}
105 = 3F -15 + 2F + 1F
105 = 6F - 15
120 = 6F
F =20
Now that we get the value of F, now we can substitute into Eqn 2 to find H
H = F -5
H = 20 - 5
H = 15
So, The number of three-point baskets from the substitution method is 15.
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