Question 93850
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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Stones: a, b, c, d, e; (smallest to largest)
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Write an equation for each statement:
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Five stones together weigh 24 pounds. 
Eq1: a + b + c + d + e = 2
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The middle one weighs 4 times as much as the smallest.
Eq2: c = 4a
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The largest weighs 3 times as much as the second smallest.
Eq3: e = 3b
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The second smallest weighs 3 times as much as the smallest. 
Eq4: b = 3a
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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
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Look at Eq3:
e = 3b
e = 3(3a) from Eq4
e = 9a
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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
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Find the rest:
b = 3a
b = 3
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c = 4a lb
c = 4 lb
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d = 7a
d = 7 lb
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e = 9a
e = 9 lb
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Check: 1 + 3 + 4 + 7 + 9 = 24
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