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Dwayne planted 70 acres with two types of beans: navy and pi
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14 Jun 2018, 14:26
14 Jun 2018, 14:26
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Question Stats:
69% (02:11) correct
30% (02:26) wrong based on 56 sessions
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Dwayne planted 70 acres with two types of beans: navy and pinto. Each acre of navy beans yielded 27 bushels and each acre of pinto beans yielded 36 bushels. If Dwayne grew twice as many bushels of pinto beans as navy beans, how many acres of pinto beans did he plant?
(A) 28
(B) 30
(C) 35
(D) 40
(E) 42
(A) 28
(B) 30
(C) 35
(D) 40
(E) 42
Re: Dwayne planted 70 acres with two types of beans: navy and pi
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05 Jul 2018, 06:49
05 Jul 2018, 06:49
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Expert Reply
Explanation
This question is difficult to translate. Begin by finding two things that are equal, and build an equation around that equality. Dwayne grew twice as many bushels of pinto beans as navy beans:
2(bushels of navy beans) = (bushels of pinto beans)
Break that down further:
bushels of navy beans = acres of navy beans × bushels per acre of navy beans
bushels of pinto beans = acres of pinto beans × bushels per acre of pinto beans
So:
2(acres of navy beans × bushels per acre of navy beans) = (acres of pinto beans × bushels per acre of pinto beans)
“Each acre of navy beans yielded 27 bushels and each acre of pinto beans yielded 36 bushels”:
2 × 27 × (acres of navy beans) = 36 × (acres of pinto beans)
Number of acres planted with pinto beans = p
Number of acres planted with navy beans = 70 – p
2 × 27(70 – p) = 36p
54(70 – p) = 36p
3,780 – 54p = 36p
3,780 = 90p
p = 42
Check the answer. If Dwayne planted 42 acres of pinto beans, he planted 28 acres of navy beans. The yield of pinto beans was 42 × 36 = 1,512 bushels. The yield of navy beans was 28 × 27 = 756 bushels, which was half the yield of pinto beans.
This question is difficult to translate. Begin by finding two things that are equal, and build an equation around that equality. Dwayne grew twice as many bushels of pinto beans as navy beans:
2(bushels of navy beans) = (bushels of pinto beans)
Break that down further:
bushels of navy beans = acres of navy beans × bushels per acre of navy beans
bushels of pinto beans = acres of pinto beans × bushels per acre of pinto beans
So:
2(acres of navy beans × bushels per acre of navy beans) = (acres of pinto beans × bushels per acre of pinto beans)
“Each acre of navy beans yielded 27 bushels and each acre of pinto beans yielded 36 bushels”:
2 × 27 × (acres of navy beans) = 36 × (acres of pinto beans)
Number of acres planted with pinto beans = p
Number of acres planted with navy beans = 70 – p
2 × 27(70 – p) = 36p
54(70 – p) = 36p
3,780 – 54p = 36p
3,780 = 90p
p = 42
Check the answer. If Dwayne planted 42 acres of pinto beans, he planted 28 acres of navy beans. The yield of pinto beans was 42 × 36 = 1,512 bushels. The yield of navy beans was 28 × 27 = 756 bushels, which was half the yield of pinto beans.
Re: Dwayne planted 70 acres with two types of beans: navy and pi
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09 Jul 2019, 02:15
09 Jul 2019, 02:15
sandy wrote:
Dwayne planted 70 acres with two types of beans: navy and pinto. Each acre of navy beans yielded 27 bushels and each acre of pinto beans yielded 36 bushels. If Dwayne grew twice as many bushels of pinto beans as navy beans, how many acres of pinto beans did he plant?
(A) 28
(B) 30
(C) 35
(D) 40
(E) 42
(A) 28
(B) 30
(C) 35
(D) 40
(E) 42
any easy way to solve it?
