Maral has 6500 tugriks, and Herlen needs 6300 tugriks. They together still need 300 tugriks to buy the notebook. What is the price of the notebook?

AlgebraWord ProblemLinear EquationsProblem Solving
2025/4/26

1. Problem Description

Maral has 6500 tugriks, and Herlen needs 6300 tugriks. They together still need 300 tugriks to buy the notebook. What is the price of the notebook?

2. Solution Steps

Let xx be the price of the notebook.
Maral has 6500 tugriks.
Herlen needs 6300 tugriks, which means Herlen has x6300x - 6300 tugriks.
Together they need 300 more tugriks, so 6500+(x6300)+300=x6500 + (x - 6300) + 300 = x.
Simplify the equation:
6500+x6300+300=x6500 + x - 6300 + 300 = x
x+500=xx + 500 = x, this is wrong. The correct equation is:
6500+x6300=x3006500 + x - 6300 = x - 300
x+200=xx + 200 = x, which is impossible.
The problem statement says that Maral has 6500 tugriks, and Herlen needs 6300 tugriks. If they buy together, they are still short 300 tugriks.
So, if Maral and Herlen combined their money, they still need 300 tugriks to buy the notebook.
Let the price of the notebook be xx.
Maral has
6
5
0

0. Herlen is short 6300, so he has $x - 6300$.

Their combined money is 6500+(x6300)6500 + (x - 6300).
They are short 300, so 6500+x6300+300=x6500 + x - 6300 + 300 = x. This is 6500+(x6300)=x3006500 + (x-6300) = x - 300.
6500+x6300=x3006500 + x - 6300 = x - 300
x+200=x300x + 200 = x - 300
This again yields an impossible equation.
The problem statement means that Maral has 6500 tugriks less than the price of the notebook, and Herlen has 6300 tugriks less than the price of the notebook. Together, they have 300 tugriks less than the price of the notebook.
So, x6500+x6300=x300x - 6500 + x - 6300 = x - 300.
2x12800=x3002x - 12800 = x - 300
2xx=128003002x - x = 12800 - 300
x=12500x = 12500.

3. Final Answer

A. 12500