SOLUTION: 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 oth

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
:
Write equations for each statement:
;
The products of three pairs of numbers are equal.
ab = cd = ef
:
One number in the second pair is 2 bigger, and
c = (a+2)
:
"one in the third pair is 3 bigger, than the first number in the 1st pair"
e = (a+3)
:
"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)
:
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
:
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
:
c = (a+2)
c = 2 + 2
c = 4
:
e = (a+3)
e = 2 + 3
e = 5
:
b = 6a + 18
b = 6(2) + 18
b = 12 + 18
b = 30
:
d = b - 15
d = 30 - 15
d = 15
:
f = b - 18
f = 30 - 18
f = 12
:
So be have 3 pairs, note the products all = 60
a=2;b=30
c=4;d=15
e=5;f=12

RELATED QUESTIONS
one number is one-third of a second number and one fifth of a third number.If the sum of... (answered by sachi)

The sum of three numbers is -2. One number is 2 times another. The quotient of another... (answered by advanced_Learner)

There are 5 pairs of socks in a drawer. 2 Blue pairs, 2 Black pairs and one gray pair.... (answered by edjones)

The sum of three numbers is 4. the first number is one-fourth of the second number and... (answered by Cromlix)

Find two consecutive odd numbers such that the sum of three-sevenths of the first number... (answered by checkley71)

The sum of three numbers is 71. The second number is twice the first number, and the... (answered by macston)

The sum of the Three Numbers is 55. The second number is twice the first number, and the... (answered by rfer)

Twice the first number is eleven more than the sum of the other two numbers. The sum of... (answered by mananth)

1. The fifth number plus the third number equals 2. The fourht number is one more than... (answered by mananth)