We can bring the ratios to a similar form, because 2:5 is the same as 4:10 (we can mupltiply rations by the same number)
so one ratio is 4:10 and the other is 4:15 and the difference is is 75 beads
in this ratio, we can see each number corresponding to a "unit" of beads: that means that what changed is that Patricia now has 5 more such groups (15-10=5), and since she has 75 beads more each unit must be 75/5=15.
so afterwards (and before) Karen had 4 such units, that is 60, and Patricia before had 10 such units, that is 150.
Prime factorization always singles down to prime numbers. The following factorization is not a prime factorization because the factors are not all prime. For example, 22 is not prime.
8 because all elements after nitrogen have not only two energy levels, they also find it easier to just get rid of electrons than to absorb electrons to get to 8 electrons.
