Greatest common factor (or denominator) is 6,
least common multiple is 180
hmm
(note:
I spent like 30 mins trying to use a math only of finding the values
but it didn't work so I did a force brute and elimination method
explained below)
so
a and b must be multiples of 6
so list all the multiples of 6
wait
180=6*30
and 30's factors are 1,2,3,5,6,10,15,30 so only list the numbers that
are the result of multiplying 6 and any of those numbers in that list
(so we can have the lcm of 180)
so
6*1=6
6*2=12
6*3=18
6*5=30
6*6=36
6*10=60
6*15=90
6*30=180
these are our possible candidates for the 2 numbers
now we must find the pair that has a GCD of only 6
doing the math is long and tedious so do it yourself (trial and error)
we see that our choices that fulfill both requirements (GCD of 6 and LCM of 180) are
90&12
60&18
30&36
sum them to find the least one
90+12=102
60+18=78
30+36=66
the least possible sum is 66
Answer: The answer should be B
Let D be dogs and C be cats
<em>dogs, d, is initially five less than twice the number of cats, c</em>
D + 5 = 2C
<em>If she decides to add three more of each, the ratio of cats to dogs will be</em>
D + 8 = 2C + 3
<em>Could Bea's Pet Shop initially have 15 cats and 20 dogs?</em>
Simply plug in the numbers
20 + 5 = 2(15)
This is clearly not true: 25 does not equal 30
<em />
<em />
