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07 Sep 2017, 22:39
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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

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Updated on: 08 Sep 2017, 16:51
Bunuel wrote:
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. 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

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Originally posted by generis on 08 Sep 2017, 07:40.
Last edited by generis on 08 Sep 2017, 16:51, edited 1 time in total.
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08 Sep 2017, 12:12
L+G = 8,000--- (1)
1/4L+3/5G = 2,875----(2)

L = 5,500 (B)