To solve this problem, we need to set up an equation based on the definition of average atomic mass. The average atomic mass is the sum of the masses of its isotopes, each multiplied by the relative abundance (as a decimal).

Let's denote the relative abundance of 16^8X as x and the relative abundance of 18^8X as y. Since these are the only two isotopes, we know that x + y = 1.

We also know that the average atomic mass of 16.2 u is the sum of the masses of the isotopes, each multiplied by its relative abundance. So, we can set up the equation:

16x + 18y = 16.2

We now have a system of two equations, and we can solve it step by step:

1. x + y = 1
2. 16x + 18y = 16.2

First, multiply the first equation by 16:

16x + 16y = 16

Subtract this from the second equation:

16x + 18y = 16.2
- (16x + 16y = 16)
-------------------
0x + 2y = 0.2

Solve for y:

2y = 0.2
y = 0.2 / 2
y = 0.1

Substitute y = 0.1 into the first equation:

x + 0.1 = 1
x = 1 - 0.1
x = 0.9

So, the relative abundances of the isotopes 16^8X and 18^8X are 90% and 10%, respectively.

Question

To solve this problem, we need to set up an equation based on the definition of average atomic mass. The average atomic mass is the sum of the masses of its isotopes, each multiplied by the relative abundance (as a decimal).

Let's denote the relative abundance of 16^8X as x and the relative abundance of 18^8X as y. Since these are the only two isotopes, we know that x + y = 1.

We also know that the average atomic mass of 16.2 u is the sum of the masses of the isotopes, each multiplied by its relative abundance. So, we can set up the equation:

16x + 18y = 16.2

We now have a system of two equations, and we can solve it step by step:

1. x + y = 1
2. 16x + 18y = 16.2

First, multiply the first equation by 16:

16x + 16y = 16

Subtract this from the second equation:

16x + 18y = 16.2
- (16x + 16y = 16)
-------------------
0x + 2y = 0.2

Solve for y:

2y = 0.2
y = 0.2 / 2
y = 0.1

Substitute y = 0.1 into the first equation:

x + 0.1 = 1
x = 1 - 0.1
x = 0.9

So, the relative abundances of the isotopes 16^8X and 18^8X are 90% and 10%, respectively.

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