Explanation

Since Beth is 12 years younger than Alan, you can write:

\(B = A - 12\)

To translate “in 20 years, Beth will be 80% of Alan’s age,” make sure that Beth becomes B + 20 and Alan becomes A + 20 (if you will be doing other operations to these values, put parentheses around them to make sure the rules of PEMDAS are not violated):

\(B + 20 = 0.8(A + 20)\)

\(B + 20 = 0.8A + 16\)

\(B + 4 = 0.8A\)

Since the first equation is already solved for B, plug (A – 12) into the simplified version of the second equation in place of B:

\(B + 4 = 0.8A\)

\((A - 12) + = 0.8A\)

\(A - 8 = 0.8A\)

\(0.2A - 8 = 0\)

\(0.2A = 8\)

\(A = 40\)

Alan is 40. Since B = A – 12, Beth is 28.

Check the answer. In 20 years, Beth will be 48 and Alan will be 60, and it is true that 48 is 80% of 60.

Hence the answer is 28