Question

If the the sum of the two numbers is 177 but one number is 3 less than another number​

Answer 1

Answer:

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

Answer 2

Step-by-step explanation:

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