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Question 203187: The products of three pairs of numbers are equal. One number in the second pair is 2 bigger, and one in the third pair is 3 bigger, than the first number in the first pair. The other numbers in the second and third pairs are respectively 15 and 18 less than second number of the first pair. Find each pair.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Three pairs of number: a,b; c,d; e,f
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Write equations for each statement:
;
The products of three pairs of numbers are equal.
ab = cd = ef
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One number in the second pair is 2 bigger, and
c = (a+2)
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"one in the third pair is 3 bigger, than the first number in the 1st pair"
e = (a+3)
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"The other numbers in the second and third pairs are respectively 15 and 18 less
than second number of the first pair."
d = (b-15)
f = (b-18)
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Find each pair
:
ab = cd
Substitute for c and d
ab = (a+2)(b-15)
Foil
ab = ab - 15a + 2b - 30
ab's cancel rewite this to:
2b - 15a = 30
:
ab = ef
Substitute for e and f
ab = (a+3)(b-18)
FOIL
ab = ab - 18a + 3b - 54
ab's cancel rewrite this to:
3b - 18a = 54
Simplify divide by 3
b - 6a = 18
b = 6a + 18
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Substitute (6a+18) for b in the equation: 2b - 15a = 30
2(6a+18) - 15a = 30
12a + 36 - 15a = 30
12a - 15a = 30 - 36
-3a = -6
a = +2
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c = (a+2)
c = 2 + 2
c = 4
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e = (a+3)
e = 2 + 3
e = 5
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b = 6a + 18
b = 6(2) + 18
b = 12 + 18
b = 30
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d = b - 15
d = 30 - 15
d = 15
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f = b - 18
f = 30 - 18
f = 12
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So be have 3 pairs, note the products all = 60
a=2;b=30
c=4;d=15
e=5;f=12
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