Question 203187
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