SOLUTION: Aunt Alice gave each of her three nieces a number of silver dollars equal to their ages. The youngest felt that this was unfair. They agreed to redistribute the money. The youngest
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Question 12331: Aunt Alice gave each of her three nieces a number of silver dollars equal to their ages. The youngest felt that this was unfair. They agreed to redistribute the money. The youngest would split half of her silver dollars evenly with the other two sisters. The middle would then give each of the others 4 silver dollars. Finally, the oldest was to split half of her dollars equally between the two younger sisters. After exchanging the money, each girl had 16 silver dollars. How old are the sisters? (Their ages = 48)
MUST HAVE PROCESS
Answer by bonster(299) (Show Source): You can put this solution on YOUR website!
youngest=x
middle=y
oldest=z
The youngest kept half and gave 1/4 each to her sisters
x:
y:Y+
z:Z+
The middle gave the oldest and youngest 4 each
x:+4
y:Y+-8
z:Z++4
the oldest kept half z so (Z++4) becomes:++2
she gives half of that to each sister so they receive: (++1)
x:+4+(++1)=16
y:Y+-8+(++1)=16
z:++2=16
+4+(++1)=16 <--subtract and 4 from both sides
(++1)=16-4-
(++1)=12-
y+-8+(++1)=16 <--subtract y and and add 8 to both sides
(++1)=16+8-y-
(++1)=24-y-
since 12- and 24-y- both equal (++1), you can equate them and solve for y:
12-=24-y-
12-=24-y- <--add to both sides
12=24-y+ <--add y to both sides
12+y=24+ <--subtract 12 from both sides
y=12+
to solve for z:
++2=16 <--subtract 2 from both sides
+=14 <--subtract from both sides
=14- <--multiply both sides by 2
z=28-
plug it back to x+y+z=48
x+(12+)+(28-)=48
x+-+12+28=48
x+40=48
x=8
since the youngest=x, she is 8 years old
middle y=(12+)=12+=12+2=14
oldest z=28-=28-=28-2=26
They are 8, 14, and 26 years old.
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