Question

1/5 of a certain number is added to 5½ the same as when ⅙ of the number that is subtracted from 30⅖find the number​

Answer 1

Explanation:

1%2F5n + 51%2F5 = 302%2F5 - 1%2F6n

make the 3rd term an improper fraction

1%2F5n + 51%2F5 = 152%2F5 - 1%2F6n

multiply equation by 30, cancel the denominators, resulting in:

6n + 6(51) = 6(152) - 5n

6n + 306 = 912 - 5n

6n + 5n = 912 - 306

11n = 606 is the number

n = 606/11

n = 55 1/11

Answer 2

68

Explanation:

let unknown number be x

⅕x + 5½= 30⅖ - ⅙x

⅕x + 11/2= 152/5 - ⅙x

collect like terms

⅕x+⅙x= 152/5 - 11/2

`(11)/(30)x = (249)/(10)`

cross multiply

30 * 249=(11 * 10)x

7470=110x

x=7470/110

x= 68