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The integers x and y are greater than 1. If (4x)(7y) = 756,
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15 May 2016, 18:09
15 May 2016, 18:09
2
Expert Reply
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Question Stats:
87% (01:14) correct
12% (02:07) wrong based on 149 sessions
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The integers x and y are greater than 1. If \((4x)(7y) = 756\), what is the value of \(x + y\) ?
Show: :: x+y=
12
Practice Questions
Question: 17
Page: 65
Question: 17
Page: 65
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Re: The integers x and y are greater than 1. If (4x)(7y) = 756,
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27 Dec 2019, 07:13
27 Dec 2019, 07:13
7
sandy wrote:
The integers x and y are greater than 1. If \((4x)(7y) = 756\), what is the value of \(x + y\) ?
Show: :: x+y=
12
GIVEN: \((4x)(7y) = 756\)
Simplify: \(28xy = 756\)
Divide both sides by 28 to get \(xy = 27\)
Since x and y are positive integers, there are only four possible solutions:
#1) x = 1 & y = 27
#2) x = 3 & y = 9
#3) x = 9 & y = 3
#4) x = 27 & y = 1
Since x and y are greater than 1, only cases #2 and #3 are possible.
In both cases, \(x + y = 12\)
Answer: 12
Cheers,
Brent
General Discussion
Re: The integers x and y are greater than 1. If (4x)(7y) = 756,
[#permalink]
15 May 2016, 18:12
15 May 2016, 18:12
4
Expert Reply
Explanation
You can solve the given equation, (4x)(7y) = 756, for the product xy:
\((4x)(7y)=756\)
\(28xy = 756\)
\(xy =27\)
Using the prime factorization 3 and 9 are the only two integers greater than 1 whose product is 27. So x + y = 12, and the correct answer is 12.
You can solve the given equation, (4x)(7y) = 756, for the product xy:
\((4x)(7y)=756\)
\(28xy = 756\)
\(xy =27\)
Using the prime factorization 3 and 9 are the only two integers greater than 1 whose product is 27. So x + y = 12, and the correct answer is 12.
