Question

Xian and his cousin Kai both collect stamps. Xian has 60 stamps, and Kai has 68 stamps. The boys recently joined different stamp-collecting clubs. Xian's club will send him 20 new stamps per month. Kai's club will send him 16 new stamps per month. After how many months will Xian and Kai have the same number of stamps? How many stamps will each have?

Answer 1

To solve this problem, let us take it in a step wise process. Here, we take each sentence and mathematically construe it;

• Sentence 1: Xian and his cousin Kai both collect stamps

We have two people, Xian and Kai collecting stamps.

Let us represent:

Xian as X

Kai as K

• Sentence 2: Xian has 60 stamps, and Kai has 68 stamps;

Number of stamps collected by X = 60 stamps

Number of stamps collected by K = 68 stamps

• Sentence 3: they joined a new club

• Sentence 4: Xian's club will send him 20 new stamps per month:

let the number of months they will send xian 20 new stamps = p months

Number of stamps = 20xp = 20p

• Sentence 5: Kai's club will send him 16 new stamps per month;

let the number of months they will send kai 16 new stamps = q months

Number of stamps = 16 x q = 16q

Problem;

After how many months will they have same number of stamps:

Number of Kai's stamp = Number of Xian's stamp

Number of Kai's stamp = 68 + 16q

Xian's stamp = 60 + 20p

So; 68 + 16q = 60 + 20p

From the problem, we know that p and q months must be the same for them to have equal number of stamps.

i.e p = q;

So;

68 + 16p = 60 + 20p

68 - 60 = 20p - 16p

8 = 4p

P= 2;

The number of months is 2 .

I. After two month, Xian and Kai will have equal number of stamps

II. Number of stamps each will receive after two months;

For Xian = 20 x p = 20 x 2 = 40 stamps

For Kai = 16 x q = 16 x p = 16 x 2 = 32 stamps