Jamal received a financial aid package of $8000 that consisted of loans and grants. If one-fourth of the loan money and three-fifths of the grant money were designated for personal living expenses, which amounted to $2875, how much money did Jamal receive in loans?

A. 6000
B. 5500
C. 3500
D. 2500
E. 1800
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Weighted values, similar to mixtures, solving for loans. An $8000 loan package consisted of loans and grants.

L + G = 8000
G = 8000 - L

One-fourth of L and three-fifths of G were designated for personal living expenses, which totaled $2875

\(\frac{1}{4}\)L + \(\frac{3}{5}\)G = 2875

\(\frac{1}{4}\)L + \(\frac{3}{5}\)(8000 - L) = 2875

\(\frac{1}{4}\)L + 4800 - \(\frac{3}{5}\)L = 2875

4800 - 2875 = \(\frac{3}{5}\)L - \(\frac{1}{4}\)L

1925 = \(\frac{7}{20}\)L

1925 * \((\frac{20}{7})\) = L

5500 = L

Answer B
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L+G = 8,000--- (1)
1/4L+3/5G = 2,875----(2)

L = 5,500 (B)
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