Question

Xian and his cousin Kai both collect stamps. Xian has 64 stamps, and Kai has 72 stamps. The boys recently joined different stamp-collecting clubs. Xian's club will send him 12 new stamps per month. Kai's club will send him 8 new stamps per month. After how many months will Xian and Kai have the same number of stamps? How many stamps will each have? After __ months Xian and his cousin will have ___stamps each.

Answer 1

After  2 months Xian and his cousin will have 88 stamps each.

Explanation

Suppose, Xian and Kai will have the same number of stamps after $t$ months.

Xian has 64 stamps, and Kai has 72 stamps. Xian's club will send him 12 new stamps per month and Kai's club will send him 8 new stamps per month.

So, the total number of stamps Xian will have after $t$ months $=64+12t$

and the total number of stamps kai will have after $t$ months $= 72+8t$

As, they will have same number of stamps after $t$ months, so...

$64+12t= 72+8t\\ \\ 12t-8t= 72-64\\ \\ 4t= 8\\ \\ t=\frac{8}{4}=2$

So, they will have same number of stamps after 2 months.

If $t=2$, then....

$64+12t=64+12(2)= 64+24=88$

and $72+8t= 72+8(2)= 72+16= 88$

So, each will have 88 stamps after 2 months.