SOLUTION: Sarah is 6 years more than 3 times as old as Denise. In 14 years the sum of thier ages will be 82. How old is Denise now?

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Question 103836: Sarah is 6 years more than 3 times as old as Denise. In 14 years the sum of thier ages will be 82. How old is Denise now?
Found 2 solutions by MathLover1, Earlsdon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let Sarah's age be x, and Denise's age be y.
given information:
x+%2B+y+%2B+14+=+82
x=3y%2B6+
so, now substitute x with 3y+%2B+6 and find y
4y+%2B+14+=+82
4y+=+82+%96+14
y+=+68%2F4
y+=+15.5 Denise is 15.5 years old now
x+=3%2A15.5+%2B+6+=+52.5 and Sarah is 52.5 years old now
in 14 years from now the sum of thier ages will be
52.5+%2B+15.5+%2B+14+=+82

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let S = Sarah's present age and D = Denise's present age.
From the problem description, you can write:
1) highlight%28S+=+3D%2B6%29 "Sarah is 6 years more than 3 times as old as Denise"
2) %28highlight%28S%29%2B14%29+%2B+%28D%2B14%29+=+82 "In 14 years, the sum of their ages will be 82"
Substitute the S from equation 1) into equation 2) and solve for D.
2a) %28highlight%283D%2B6%29%2B14%29+%2B+%28D%2B14%29+=+82 Simplify.
4D%2B34+=+82 Subtract 34 from both sides.
4D+=+48 Divide by both sides by 4.
D+=+12 This is Denise's present age.
S+=+3D%2B6
S+=+3%2812%29%2B6
S+=+36%2B6
S+=+42 This is Sarah's present age.