If the reciprocal of a number is multiplied by 1 less than the original number, the results exceed 1/2 the reciprocal of the original number by 5/8. Find the number.

  4

Step-by-step explanation:

Let's try this a different way than perhaps the usual way. Let r represent the reciprocal of the number.

  r(1/r -1) -1/2r = 5/8

  1 -r -1/2r = 5/8 . . . . . . eliminate parentheses

  -3/2r = -3/8 . . . . . . . . collect terms, subtract 1

  (-3/2)/(-3/8) = 1/r = 4 . . . . . divide by (-3/8)r because we actually want 1/r

The number is 4.

Check

The reciprocal of the number is 1/4.

1 less than the original number is 4 -1 = 3. The product of these is 3/4.

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Half the reciprocal of the original number is (1/2)(1/4) = 1/8.

Then the difference between these is ...

  3/4 -1/8 = (6 -1)/8 = 5/8 . . . . as required.

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40