Kim, Mei and yante collect stamps. Kim and Mei have 220 stamps more than Yanti. Yanti and Mei have 140 stamps more than Kim. Kim and Yanti have 500 stamps. How many stamps does Mei have?
K+M=220+Y
Y+M=140+K
220+140=360
2M=360
M=360÷2=180
M=180
Umm... so Steve what's the final answer and how did u get that ?
Answer is 180
To find out how many stamps Mei has, we can start by setting up some equations based on the given information.
Let's assume that Yanti has x stamps.
According to the problem, Kim and Mei have 220 stamps more than Yanti, so Kim and Mei together would have x + 220 stamps each.
It is also mentioned that Yanti and Mei have 140 stamps more than Kim, so Yanti and Mei together would have x + 140 stamps each.
Finally, it is stated that Kim and Yanti together have 500 stamps, so Kim + Yanti = 500.
We can now form equations based on the given information:
1. Kim + Mei = 2 * (Yanti) + 220
2. Yanti + Mei = 2 * (Kim) + 140
3. Kim + Yanti = 500
To solve these equations, we can start by rewriting equation 1 and equation 2:
Kim + Mei = 2Yanti + 220 ---> Kim - Mei = 2Yanti + 220
Yanti + Mei = 2Kim + 140 ---> -Yanti + Mei = 2Kim + 140
Now, we can add equation 1 and equation 2:
(Kim - Mei) + (-Yanti + Mei) = (2Yanti + 220) + (2Kim + 140)
By simplifying:
Kim - Mei - Yanti + Mei = 2Yanti + 2Kim + 220 + 140
Kim - Yanti = 2Kim + 2Yanti + 360
Now, let's rearrange the equation:
Kim - 2Kim + Yanti - 2Yanti = 360
-Kim - Yanti = 360
Substituting equation 3 (Kim + Yanti = 500), we can rewrite the equation as:
-500 + Yanti = 360
By solving for Yanti:
Yanti = 500 - 360
Yanti = 140
Now that we know Yanti has 140 stamps, we can substitute this value into equation 3 to find the value of Kim:
Kim + 140 = 500
Kim = 500 - 140
Kim = 360
Finally, to find the number of stamps Mei has, we can substitute our values for Kim and Yanti into either equation 1 or equation 2:
Mei = 2Yanti + 220
Mei = 2(140) + 220
Mei = 280 + 220
Mei = 500
Therefore, Mei has 500 stamps.
how to solve the problem
Thx. For the answer now I am finished with math homework.
k+y = 500
k+m = y+220
y+m = k+140
Or, in more standard format,
k+m = 500
k+m-y = 220
-k+m+y = 140
These are easy to solve.