One number is 3 less than another number. If the sum of the two numbers is 177, find each number.
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Audra C. asked • 07/13/17
What's the answer One number is 3 less than another. The sum of their reciprocals is equal to 7 divided by the product of the two numbers. Find the numbers.
One number is 3 less than another. The sum of their reciprocals is equal to 7 divided by the product of the two numbers. Find the numbers.
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Kathy M. answered • 07/13/17
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One number is 3 less than another.
a = one number
a-3 = the other number
The sum of their reciprocals is equal to 7 divided by the product of the two numbers.
1/a = reciprocal of one number
1/ (a-3) = the reciprocal of the other number
7 / [a(a-3) ] = 7 divided by the product of the two numbers
1/a + 1/(a-3) = 7 / [a(a-3) ] the sum of the reciprocals
Find the numbers.
a(a-3) [1/a + 1/(a-3) ] = a(a-3) (7 / [a(a-3)] ) multiply both sides by the common denominator a(a-3)
[a(a-3)(1)]/a + a(a-3)(1)]/(a-3) = a(a-3) (7 / [a(a-3)] ) distribute common denominators to all terms
[a(a-3)(1)]/a + a(a-3)(1)]/(a-3) = a(a-3) (7 / [a(a-3)] ) cancel common factors in terms to eliminate denominators
a-3 + a = 7 combine like terms on left and add 3 to both sides
2a = 10 divide both sides by 2
a = 5
Solution:
a = one number = 5
a-3 = the other number = 5-3 = 2
Check:
1/5 + 1/2 = 2/10 + 5/10 = 7/10
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Answer:
The two numbers are 90 and 87
Step-by-step explanation:
Let one number be (x)
Then the other number must be (x-3)
Given that when,
x + (x-3) = 177
Therefore (2x - 3) = 177
2x = 180
x = 90
(x-3) = 90 - 3 = 87
Therefore one number is 90 whereas the other number is 87.
Hope it helps you.