SOLUTION: Kate is three years less than twice as old as her brother Brett. Next year Bretts age will be three fourths Kates age. How old is each now?

Question 256628: Kate is three years less than twice as old as her brother Brett. Next year Bretts age will be three fourths Kates age. How old is each now?

Found 3 solutions by stanbon, checkley77, palanisamy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Kate is three years less than twice as old as her brother Brett. Next year Bretts age will be three fourths Kates age. How old is each now?
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Equations:
K = 2B-3
(B+1)= (3/4)(K+1)
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Rearrange:
4B+4 = 3K+3
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K = 2B-3
K = (4/3)B+1
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Solve 2B-3 = (4/3)B+1
(2/3)B = 4
B = 6 yrs (Brett's age NOW)
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Since K = 2B-3, K =2*6-3 = 9 (Katie's age NOW)
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Cheers,
Stan H.
Answer by checkley77(12844)   (Show Source): You can put this solution on YOUR website!
K=X
B=2X-3
NEXT YEAR:
X+1=(2X-3+1)*3/4
X+1=(6X-9+3)/4
X+1=(6X-6)/4 CROSS MULTIPLY
4(X+1)=6X-6
4X+4=6X-6
4X-6X=-6-4
-2X=-10
X=-10/-2
X=5 ANS. FOR KATE'S AGE NOW.
2*5-3=10-3=7 ANS. FOR BRETT'S AGE NOW.
PROOF:
5+1=(7+1)3/4
6=8*3/4
6=24/4
6=6
Answer by palanisamy(496)   (Show Source): You can put this solution on YOUR website!
Let the age of Kate =x
Let the age of Brett =y
Given, Kate is three years less than twice as old as her brother Brett.
x = 2y-3 ...(1)
Also, next year Bretts age will be three fourths Kates age.
y+1 = (3/4)*(x+1)
4(y+1) = 3(x+1)
4y+4 = 3x+3
Put x = 2y-3 in (2).
4y+4 = 3(2y-3)+3
4y+4 = 6y-9+3
4y-6y = -9+3-4
-2y = -10
y = -10/(-2)
y = 5
Substituting in (1),
x = 2*5-3 = 10-3 = 7
Therefore, the age of Kate = 7
and the age of Brett = 5

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