danielle plays softball and basketball. however because she like basketball more, she spends 3 times as long playing basketball than she does playing softball. if she spends 18 hours a week playing these sports, how much time does she devote tp playing basketball?
a)13 hours
b)13.5 hours
c)12 hours
d)4.5 hours
tell me how to get the answer and label variables you use please
b=3s, so
s+3s=18
4s=18
s=4.5
so, b=3s=13.5
(b)
To solve this problem, we can set up a system of equations. Let's label the time Danielle spends playing softball as 's' and the time she spends playing basketball as 'b'.
From the given information, we know that Danielle spends 3 times as long playing basketball than she does playing softball. So, we can write an equation:
b = 3s ---(Equation 1)
We also know that Danielle spends a total of 18 hours a week playing both sports. Therefore, we can write a second equation to represent the total time she spends:
s + b = 18 ---(Equation 2)
Now we have a system of equations with two unknowns. We can solve this system by substituting Equation 1 into Equation 2.
Substituting b = 3s from Equation 1 into Equation 2, we have:
s + 3s = 18
4s = 18
s = 18/4
s = 4.5
So, Danielle spends 4.5 hours playing softball.
To find the time she devotes to playing basketball, we can substitute the value of s back into Equation 1:
b = 3(4.5)
b = 13.5
Therefore, Danielle devotes 13.5 hours to playing basketball, which is option (b).