Grandpa age is 6 years less then 6 time juniors age the sum of their age is 78 find the each of their age

Grandpa is 6 years less than 6 times junior’s age. Let’s translate that in math form.
6 times juniors age(j) minus 6
6j - 6

The sum of their games is 78. Add Junior’s age with Grandpa’s.
6j-6 +j = 78.

Now add like terms and solve for j.
7j-6 = 78
+6 +6

7j= 84
———-
7
j= 12

Junior is 12 years old.

Substitute j to Grandpa’s equation.

6(12) - 6
72 -6
66

Grandpa is 66 years old.

1/x + 1/(x+2) = 9/40 > don't forget parentheses) 

Multiply both sides by 40x(x+2) 

40x(x+2) (1/x + 1/(x+2)) = 40x(x+2) * 9/40 
40(x+2) + 40x = 9x(x+2) 
40x + 80 + 40x = 9x² + 18x 
9x² + 18x = 80x + 80 
9x² − 62x − 80 = 0 
(9x + 10) (x − 8) = 0 
x = −10/9, x = 8 

Since x is an integer, then x = 8, and the two consecutive even integers are 8 and 10 

 

Check: 

1/8 + 1/10 = 5/40 + 4/40 = 9/40 ---> ok