SOLUTION: I have to solve this with a equation. Thanks! Five stones together weigh 24 pounds. The middle one weighs 4 times as much as the smallest. The largest weighs 3 times as much as

Algebra ->  Equations -> SOLUTION: I have to solve this with a equation. Thanks! Five stones together weigh 24 pounds. The middle one weighs 4 times as much as the smallest. The largest weighs 3 times as much as      Log On


   

Question 93850: I have to solve this with a equation. Thanks!
Five stones together weigh 24 pounds. The middle one weighs 4 times as much as the smallest. The largest weighs 3 times as much as the second smallest. The second smallest weighs 3 times as much as the smallest. The fourth smallest weighs as much as the second and third smallest together. How much does each stone weigh?
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Five stones together weigh 24 pounds. The middle one weighs 4 times as much as the smallest. The largest weighs 3 times as much as the second smallest. The second smallest weighs 3 times as much as the smallest. The fourth smallest weighs as much as the second and third smallest together. How much does each stone weigh?
:
Stones: a, b, c, d, e; (smallest to largest)
:
Write an equation for each statement:
:
Five stones together weigh 24 pounds.
Eq1: a + b + c + d + e = 2
:
The middle one weighs 4 times as much as the smallest.
Eq2: c = 4a
:
The largest weighs 3 times as much as the second smallest.
Eq3: e = 3b
:
The second smallest weighs 3 times as much as the smallest.
Eq4: b = 3a
:
The fourth smallest weighs as much as the second and third smallest together.
d = b + c
d = (3a) + (4a); from equation 2 and 4
d = 7a
:
Look at Eq3:
e = 3b
e = 3(3a) from Eq4
e = 9a
:
How much does each stone weigh?
Substitute our derived equations for the last 4 variables in Eq1:
a + b + c + d + e = 24
a + 3a + 4a + 7a + 9a = 24
24a = 24
a = 1 lb
:
Find the rest:
b = 3a
b = 3
:
c = 4a lb
c = 4 lb
:
d = 7a
d = 7 lb
:
e = 9a
e = 9 lb
:
Check: 1 + 3 + 4 + 7 + 9 = 24
:
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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Five stones together weigh 24 pounds.
The middle one weighs 4 times as much as the smallest.
The largest weighs 3 times as much as the second smallest.
The second smallest weighs 3 times as much as the smallest.
The fourth smallest weighs as much as the second and third smallest together. How much does each stone weigh?
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To avoid fraction always let the smallest be "x".
middle = 4x
2nd smallest = 3x
largest = 3*3x=9x
4th smallest = 3x+(3rd smallest)
=================
EQUATION:
x + 4x + 3x + 9x + 3x + 3rd smallest = 24
20x + 3rd smallest = 24.
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You now have two variables because you did not include any information
at the 3rd smallest.
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Cheers,
Stan H.