Question 472641: 1. Kevin and Karen are brother and sister. Kevin has twice as many sisters as he has brothers. Karen has the same number of brothers as sisters.
a. Set up a system of equations to model this situation. How did you figure out what each equation would be? Let d be the number of daughters that Kevin and Karen’s parents have, and s be the number of sons that Kevin and Karen’s parents have.
b. Solve the system of equations, showing all your work.
c. How many sisters does Kevin have?
d. How many sisters does Karen have?
e. How many brothers does Kevin have?
f. How many brothers does Karen have?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! kevin and karen are brother and sister.
d = number of daughters in the family.
s = number of sons in the family.
the number of brothers that kevin has is s-1.
the number of sisters that kevin has is d.
the number of brothers that karen has is s.
the number of sisters that karen has is d-1.
kevin has twice as many sisters as he has brothers.
this means that d = 2 * (s-1).
karen has the same number of brothers as sisters.
this means that d-1 = s.
the 2 equations we have to work with are:
d = 2 * (s-1) (first equation)
d-1 = s (second equation)
that's our system of equations.
we need to solve for either d or s and, from that, we should be able its partner.
we start with the second equation of d-1 = s.
this is the same as s = d-1.
we can substitute for s in the first equation to get:
d = 2 * (s-1) becomes:
d = 2 * ((d-1)-1) which becomes:
d = 2 * (d-2) which becomes:
d = 2*d - 4
subtract d from both sides of this equation and add 4 to both sides of this equation to get:
d = 4
if this is right, the number of daughters is 4.
we can now substitute in the second equation to solve for s.
the second equation is:
d-1 = s
since d = 4, this means that s equals 3.
we now have:
d = 4 (number of daughters)
s = 3 (number of sons)
we need to confirm these numbers are good.
the opening statement of the problem is:
1. Kevin and Karen are brother and sister. Kevin has twice as many sisters as he has brothers. Karen has the same number of brothers as sisters.
we know that kevin has s-1 brothers.
this means that kevin has 3 - 1 brothers which is equal to 2.
we know that kevin has d sisters.
this means that kevin has 4 sisters.
4 sisters is twice as many as 2 brothers, so the first part of the opening statement is confirmed as correct.
karen has the same number of brothers and sisters.
karen has 2 brothers which is equal to 3.
karen has d-1 sisters which is equal to 4 - 1 = 3
3 brothers is equal to 3 sisters, so the second part of the opening statement is confirmed as correct.
answers to the questions are:
c. How many sisters does Kevin have? (4)
d. How many sisters does Karen have? (3)
e. How many brothers does Kevin have? (2)
f. How many brothers does Karen have? (3)
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