SOLUTION: A, B and C are consecutive natural numbers. If 2/7 of the reciprocal of A is equal to ⅓ of the reciprocal of C, find B.

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Question 1204069: A, B and C are consecutive natural numbers. If 2/7 of the reciprocal of A is equal to ⅓ of the reciprocal of C, find B.

Found 5 solutions by ikleyn, math_tutor2020, MathLover1, MathTherapy, greenestamps:
Answer by ikleyn(52786)   (Show Source):
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A, B and C are consecutive natural numbers. If 2/7 of the reciprocal of A is equal to ⅓ of the reciprocal of C, find B.
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Let B = n; then A = n-1; C = n+1. The equation is = , or = . To solve, multiply both sides by 7*3*(n-1)*(n+1). You will get 2*3*(n+1) = 7*(n-1), 6(n+1) = 7(n-1) 6n + 6 = 7n - 7 6 + 7 = 7n - 6n 13 = n. ANSWER. The numbers are 12, 13 and 14.

Solved.

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If you read the post by @greenestamps, you will see in the third line

        "2/7 of the reciprocal of A is 7/2 times A; 1/3 of the reciprocal of C is 3/1 times C."

This statement is incorrect.
For the correct setup, read the posts of other tutors.

Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

Consecutive numbers follow one right after another.
An example would be 7,8,9.

A,B,C are consecutive natural numbers from the set {1,2,3,4,...}

Since B follows right after A, we can state: B = A+1
Also C = B+1 = (A+1)+1 = A+2

The sequence A, B, C is the same as A, A+1, A+2.

(2/7)*(reciprocal of A) = (1/3)*(reciprocal of C)
(2/7)*(1/A) = (1/3)*(1/C)
2/(7A) = (1/3)*(1/(A+2))
2/(7A) = 1/(3(A+2))
2*3(A+2) = 7A*1 .... cross multiplication
6A+12 = 7A
12 = 7A-6A
12 = A
A = 12

If A = 12, then,
B = A+1 = 12+1 = 13
C = A+2 = 12+2 = 14

In short
A = 12
B = 13
C = 14

Let's check to see if we have the right answer.
(2/7) of (1/A) = (1/3) of (1/C)
(2/7)*(1/12) = (1/3)*(1/14)
(2*1)/(7*12) = (1*1)/(3*14)
(2*1)/(7*2*6) = (1*1)/(3*14)
1/42 = 1/42
We have confirmed the answer is correct.

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Answer: B = 13

Answer by MathLover1(20850)   (Show Source):
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= { , , , , , , ……} So consecutive natural numbers are the numbers that continuously follow each other in order from the smallest number to the largest number.
let

the reciprocal of
of the reciprocal of is
the reciprocal of is
of the reciprocal of is
If of the reciprocal of is equal to of the reciprocal of , we have

...cross multiply

then

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

A, B and C are consecutive natural numbers. If 2/7 of the reciprocal of A is equal to ⅓ of the reciprocal of C, find B. Let B = B Since A, B, C are natural consecutive numbers, then A = B - 1, and C = B + 1 We then get: 2(3B + 3) = 7B - 7 ------ Cross-multiplying 6B + 6 = 7B - 7 6 + 7 = 7B- 6B 13 = B

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

You have received several responses showing valid solutions. They all use equations involving the reciprocals of A and C, because that is how the information is given.

The algebra is easier if you set up the problem differently.

2/7 of the reciprocal of A is 7/2 times A; 1/3 of the reciprocal of C is 3/1 times C.

A, B, and C are consecutive natural numbers, and we are solving for B. So A is B-1 and C is B+1. Then we have

ANSWER: B = 13

SOLUTION: A, B and C are consecutive natural numbers. If 2/7 of the reciprocal of A is equal to ⅓ of the reciprocal of C, find B.​

SOLUTION: A, B and C are consecutive natural numbers. If 2/7 of the reciprocal of A is equal to ⅓ of the reciprocal of C, find B.