AP Chem hw ? i don't understand?

Question

The problem says,

THe element europium exists in nature as two isotopes:151Eu has a mass of 150.9196 amu. and 153Eu has a mass of 152.9209 amu. The average atomic mass of europium is 151.96 amu. Calculate the relative abundance of the two europium isotopes.

All i need to know is how to solve it, or how to set it up

Thanks

Answer 1

Its a two equations two unknowns = substitution question

the two percents together as fractions = 1

x+y=1

x=1-y

subsitute in x

(1-y)*150.9196+y*152.9209=151.96 amu

y= 0.51986 =51.986% of the 152.9209 amu

There is 51.986% of the 153Eu

x+y=1 substitute in y=51.986 as 0.51986 and x =0.48014 or 48.014% 151Eu

Answer 2

This is very simple,

Let there be x% of 151 Eu and (100-x)% of 153 Eu

So,  (x*150.9196) + [(100-x)*152.9209]

       ----------------------------------------...    =  151.96

                        100

15292.09 - 15196 = x*(152.9209-150.9196)

96.09 = 2.0013*x

x = 48.013 % of 151 Eu and 51.987% of 153Eu