Abundance of isotopes based on ratios

[subopolois]

Homework Statement

how do i find abundances of isotopes of strontium if i am give their isotopic ratios and atomic masses

Homework Equations

The Attempt at a Solution

i know i have to find what the mass of each isotope is in the ratios to find the % abundance. i don't want to put up the actual numbers because i want to work this out myself. i just need a push in the right direction to get started

 

[chemisttree]

do the math on the ratios. they should sum to 1.

ie. 3:7 is 3/(3+7) or 0.3

 

[subopolois]

i should have mentioned that there are 4 isotopes, I am given 3 ratios and am told to find the abundance of each one
ie. 86Sr/88Sr= 0.12
84Sr/88Sr= 0.007
87Sr/86Sr= 2.5

i really don't know how to go about doing this

 

[symbolipoint]

The masses of the different isotopes can be assigned to variables, w, x, y, z for the Strontiums of masses 84, 86, 87, 88.

Those ratios you were given may then be stated as:
x/z = 0.12
w/z = 0.007
y/x = 2.5

All of the relative masses must sum to 1. This makes a necessary equation of this:
w + x + y + z = 1.0000

Now you have four equations using 4 unknown numbers. Those three ratio equations are convertible to linear equations, so the set of equations forms a fairly simple system of linear equations and should be fairly easily solvable.