If one half of an integer is added to one fifth of the next consecutive integer, the sum is 10. Find the integers.

1/2x + 1/5 (x + 1) = 10

1/2x + 1/5x + 1/5 = 10

5/10x + 2/10x = 10 - 1/5

7/10x = 50/5 - 1/5

7/10x = 49/5

x = 49/5 * 10/7

x = 490/35

x = 14

x + 1 = 15

ur integers are 14 and 15

Let 1st integer be x and next consecutive be x+1

1/2•x + 1/5• (x+1) = 10

x/2 + x/5 + 1/5 = 10

-1/5 - 1/5

x/2 + x/5 = 49/5

(x/2) •5/5 + (x/5) •2/2 = 49/5

5x/10 + 2x/10 = 49/5

7x/10 = 49/5

•10 •10

7x = 98

:7 : 7

x = 14 - - > 1st integer

x+1 = 14+1 = 15 - - > next consecutive integer