SOLUTION: Alexa and Brittney are sisters whose current ages have a sum of 43. Three times Alexa’s current age subtracted by four times Brittney’s current age equals the current age of their

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Question 1060974: Alexa and Brittney are sisters whose current ages have a sum of 43. Three times Alexa’s current age subtracted by four times Brittney’s current age equals the current age of their three-year-old sister, Cheryl. How old is their other sister Denise, who is 5 years younger than Brittney? Write a system of equations this situation and find its solution.
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
let the sister's present ages be:
a+, +b+, +c+, and +d+
-----------------------------------
(1) +a+%2B+b+=+43+
(2) +3a+-+4b+=+3c+
(3) +d+=+b+-+5+
------------------------
There are 4 unknowns, but there are
only 3 equations. Are you missing an equation?
As far as I know, this can't be solved as
presently stated.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Alexa and Brittney are sisters whose current ages have a sum of 43. Three times Alexa’s current age subtracted by
four times Brittney’s current age equals the current age of their three-year-old sister, Cheryl.
How old is their other sister Denise, who is 5 years younger than Brittney? Write a system of equations this situation and find its solution.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

 A +  B = 43,     (1)   ("Alexa and Brittney are sisters whose current ages have a sum of 43.")
3A - 4B =  3.     (2)   ("Three times Alexa’s current age subtracted by four times Brittney’s current age equals 
                         the current age of their three-year-old sister, Cheryl.)

====> 

From (1),  A = 43-B  ---> (substitute it into (2) )  --->  3(43-B) - 4B = 3  --->  7B = 126  --->  B = 126%2F7 = 18  --->  A = 43-18 = 25.

Alexa is 25 years old. Brittney is 18 years old.

Denise is B-5 = 18-5 = 13 years old.

Solved.