Here's how to solve this one with algebra:
Define variables for the numbers of students with and without a master’s degree.
\(y = 100 - x\)
Compute the number of students who did not get finance jobs.
\(100 - 68 = 32\)
Express the number of non-master’s students who got finance jobs as 20% of y.
\(\frac{20}{100} \times y = 0.20y\)
Express the number of finance-job students with a master’s degree as the remainder of total finance jobs.
\(68 - 0.20y\)
Compute the number of master’s-degree students among non-finance jobs as 25% of the 32 non-finance students.
\(\frac{25}{100} \times 32 = 8\)
Set the count of non-finance master’s students equal to total master’s minus finance master’s count.
\(x - \bigl(68 - 0.20y\bigr) = 8\)
Substitute y = 100 - x into the equation relating x and y.
\(x - \bigl(68 - 0.20\,(100 - x)\bigr) = 8\)
Simplify inside the parentheses and combine like terms.
\(x - \bigl(48 + 0.20x\bigr) = 8\\x - 48 - 0.20x = 8\)
Solve the linear equation for x.
\(0.80x = 56\\x = \frac{56}{0.80} = 70\)
Convert the number of master’s-degree students into a percentage of the total 100 students.
\(\frac{70}{100} \times 100\% = 70\%\)
Answer 70% (Option D)
Hope this helps!
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