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The sum of x and y is at least 2 but no more than 5. If the
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18 Mar 2018, 06:15
18 Mar 2018, 06:15
Expert Reply
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Question Stats:
56% (01:18) correct
43% (02:44) wrong based on 23 sessions
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The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y?
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
Drill 2
Question: 8
Page: 498
Question: 8
Page: 498
Re: The sum of x and y is at least 2 but no more than 5. If the
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18 Mar 2018, 07:30
18 Mar 2018, 07:30
1
Expert Reply
Explanation
Translate what you are told into algebra: 2 ≤ x + y ≤ 5 and 0 ≤ 2x + 3y ≤ 40.
By manipulating the inequalities, you find that 2 − y ≤ x ≤ 5 – y and –2x ≤ 3y ≤ 40 − 2x.
Substitute the endpoints of the values of x into the second inequality: –2(2 – y) ≤ 3y ≤ 40 − 2(2 − y) and –2(5 − y) ≤ 3y ≤ 40 − 2(5 − y).
By solving for y, the first range yields –4 ≤ y ≤ 36, and the second yields –10 ≤ y ≤ 30, meaning –10 ≤ y ≤ 36 overall.
Translate what you are told into algebra: 2 ≤ x + y ≤ 5 and 0 ≤ 2x + 3y ≤ 40.
By manipulating the inequalities, you find that 2 − y ≤ x ≤ 5 – y and –2x ≤ 3y ≤ 40 − 2x.
Substitute the endpoints of the values of x into the second inequality: –2(2 – y) ≤ 3y ≤ 40 − 2(2 − y) and –2(5 − y) ≤ 3y ≤ 40 − 2(5 − y).
By solving for y, the first range yields –4 ≤ y ≤ 36, and the second yields –10 ≤ y ≤ 30, meaning –10 ≤ y ≤ 36 overall.
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Re: The sum of x and y is at least 2 but no more than 5. If the
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01 Jun 2018, 09:27
01 Jun 2018, 09:27
1
Expert Reply
sandy wrote:
The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y?
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
We can create the following inequalities:
2 ≤ x + y ≤ 5
0 ≤ 2x + 3y ≤ 40
Multiplying the first inequality by -2, we have:
-4 ≥ -2x - 2y ≥ -10
-10 ≤ -2x - 2y ≤ -4
Adding this to 0 ≤ 2x + 3y ≤ 40, we have:
-10 ≤ y ≤ 36
Answer: C
