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Average Atomic Mass | Introduction to Chemistry

Calculate the average atomic mass of an element given its isotopes and their natural ... An element can have differing numbers of neutrons in its nucleus, but it ... masses of the element's isotopes, each multiplied by its natural abundance on Earth. ... To calculate the average mass, first convert the percentages into fractions ...

For more information, see Average Atomic Mass | Introduction to Chemistry

Average atomic mass =\frac{\Sigma\text{isotope abundance * isotope mass }}{\Sigma\text{ isotope abundance }}

= \frac{\Sigma (m_i \eta_i)}{\Sigma \eta_i}

Step 1: Calculating the isotopes abundances

Given that

Average atomic mass magnesium = 24.313 u

Mass of ^{24}_{12} Mg = 23.98504 u

Mass of ^{25}_{12} Mg = 24.98584 u

Mass of ^{26}_{12} Mg = 25.98259 u

Abundance of   ^{24}_{12} Mg = 78.99 %

Abundance of ^{25}_{12} Mg = x%

Abundance of ^{26}_{12} Mg = y% = 78.99 % + x% + y%= 100%

y% = 100% - 78.99 % - x% = 21.01% - x%

Substituting the all the values in the average atomic mass formula.

Average atomic mass = \frac{(23.98504 * 78.99) + (24.98584 * x) +(25.98259 * (21.01 - x))}{78.99 + x + 21.01 - x }

24.313 = \frac{(23.98504 * 78.99) + (24.98584 * x) +(25.98259 * (21.01 - x))}{100}

24.313 = \frac{1894.578 + 545.894 + x(24.98584 - 25.98259)}{100}

x = \frac{2440.472 - 2431.2}{0.99675}

x = 9.30

Abundance of ^{26}_{12} Mg = 21.01 - x = 21.01 - 9.30 = 11.71

Hence, Abundance of ^{25}_{12} Mg is 9.30% and Abundance of ^{26}_{12} Mg is 11.71%