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07 Sep 2017, 23:39
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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
A. 6000
B. 5500
C. 3500
D. 2500
E. 1800
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07 Sep 2017, 23:42
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Bunuel
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
A. 6000
B. 5500
C. 3500
D. 2500
E. 1800
L + G = 8000
L/4 + 3G/5 = 2875
L + 12G/5 = 11500
7G/5 = 3500
G = 2500
L = 8000-2500 = 5500
B
Bunuel
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
Weighted values, similar to mixtures, solving for loans. An $8000 loan package consisted of loans and grants.A. 6000
B. 5500
C. 3500
D. 2500
E. 1800
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
