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Jamal received a financial aid package of $8000 that consisted of loan

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Jamal received a financial aid package of $8000 that consisted of loan [#permalink]

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New post 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
Spoiler: OA

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Re: Jamal received a financial aid package of $8000 that consisted of loan [#permalink]

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New post 07 Sep 2017, 23:42
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


L + G = 8000
L/4 + 3G/5 = 2875
L + 12G/5 = 11500

7G/5 = 3500
G = 2500
L = 8000-2500 = 5500
B
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Jamal received a financial aid package of $8000 that consisted of loan [#permalink]

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New post Updated on: 08 Sep 2017, 17:51
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

Answer B
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Originally posted by generis on 08 Sep 2017, 08:40.
Last edited by generis on 08 Sep 2017, 17:51, edited 1 time in total.
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Jamal received a financial aid package of $8000 that consisted of loan [#permalink]

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New post 08 Sep 2017, 08:56
Let Jamal's loans be L and his grants is G

\(L + G = 8000\)
Multiplied by 5, \(5L + 5G = 40000\) -> (1)

\(L/4 + 3G/5 = 2875\)
\(5L + 12G = 57500\) -> (2)

(2) - (1) 7G = 17500 => G = 2500

Therefore, L = 5500(Option B)
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Re: Jamal received a financial aid package of $8000 that consisted of loan [#permalink]

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New post 08 Sep 2017, 13:12
L+G = 8,000--- (1)
1/4L+3/5G = 2,875----(2)

L = 5,500 (B)
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Re: Jamal received a financial aid package of $8000 that consisted of loan   [#permalink] 08 Sep 2017, 13:12
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Jamal received a financial aid package of $8000 that consisted of loan

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