SOLUTION: William is 2 years older than his friend Daniel. William's mother is twice as old as William and Daniel is twice as old as his sister. The age of William's mother is 34 years more

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Question 1116219: William is 2 years older than his friend Daniel. William's mother is twice as old as William and Daniel is twice as old as his sister. The age of William's mother is 34 years more than the age of Daniel's sister. Find the age of William and Daniel.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = William's age now
Let +b+%7D%7D%5D+=+Daniel%27s+age+now%0D%0ALet+%7B%7B%7B+c+ = William's mother's age now
Let +d+ = Daniel's sister's age now
-----------------------------------------
(1) +a+=+b+%2B+2+
(2) +c+=+2a+
(3) +b+=+2d+
(4) +c+=+d+%2B+34+
--------------------------
From (2) and (4)
+2a+=+d+%2B+34+
From (3)
+d+=+b%2F2+
and
+2a+=+b%2F2+%2B+34+
+4a+=+b+%2B+68+
From (1)
(1) +b+=+a+-+2+
and
+4a+=+a+-+2+%2B+68+
+3a+=+66+
+a+=+22+
and
(1) +b+=+a+-+2+
(1) +b+=+22+-+2+
(1) +b+=+20+
and
(2) +c+=+2a+
(2) +c+=+2%2A22+
(2) +c+=+44+
and
(3) +d+=+b%2F2+
(3) +d+=+20%2F2+
(3) +d+=+10+
---------------------
William is 22
Daniel is 20
----------------------
check:
(4) +c+=+d+%2B+34+
(4) +44+=+10+%2B+34+
(4) +44+=+44+
OK
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Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

William is 2 years older than his friend Daniel. William's mother is twice as old as William and Daniel is twice as old as his sister. The age of William's mother is 34 years more than the age of Daniel's sister. Find the age of William and Daniel.
Let Daniel's age be D
Then William's is: D + 2
Mother's is: 2(D + 2), or 2D + 4
Sister's is: D%2F2
We then get: matrix%281%2C3%2C+2D+%2B+4%2C+%22=%22%2C+D%2F2+%2B+34%29
matrix%281%2C3%2C+2D+-+D%2F2%2C+%22=%22%2C+30%29
4D - D = 60 ------ Multiplying by LCD, 2
3D = 60
D, or Daniel is: highlight_green%28matrix%281%2C4%2C+60%2F3%2C+%22=%22%2C+20%2C+%22years-old%22%29%29
William is: highlight_green%28matrix%281%2C4%2C+20+%2B+2%2C+%22=%22%2C+22%2C+years-old%29%29