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# A university awarded grants in the amount of either \$7,000 or \$10,000

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A university awarded grants in the amount of either \$7,000 or \$10,000  [#permalink]

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26 Feb 2017, 09:48
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45% (medium)

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61% (01:35) correct 39% (02:05) wrong based on 48 sessions

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A university awarded grants in the amount of either \$7,000 or \$10,000 to some incoming freshmen. The total amount of all such awards was \$2,300,000. Did the university award more \$7,000 grants than \$10,000 grants to its incoming freshmen?

(1) A total of 275 freshmen received grants in one of the two amounts.
(2) The amount of money awarded in \$10,000 grants was \$200,000 more than the amount of money awarded in \$7,000 grants.

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Re: A university awarded grants in the amount of either \$7,000 or \$10,000  [#permalink]

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11 Sep 2017, 02:03
1
Let no. of \$7,000 grants =a
No. of \$10,000 grants =b
\$7,000a + \$10,000b = \$2,300,000
=>7a + 10b = 2300

Find if a>b ?

(1) A total of 275 freshmen received grants in one of the two amounts.

so a+b = 275
We got 2 equations on a and b so we can find values of a and b and compare. Sufficient
equations:
a+b =275
7a + 10b = 2300

(2) The amount of money awarded in \$10,000 grants was \$200,000 more than the amount of money awarded in \$7,000 grants.

10000b = 200000 +7000a
=> 10b =200 +7a
We got 2 equations on a and b so we can find values of a and b and compare. Sufficient
equations:
10b =200 +7a
7a + 10b = 2300

Re: A university awarded grants in the amount of either \$7,000 or \$10,000   [#permalink] 11 Sep 2017, 02:03
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# A university awarded grants in the amount of either \$7,000 or \$10,000

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