Let O, M, and A represent the costs of one orange, one mango, and one apple, respectively.
According to the problem statement, the total cost of 4 oranges, 6 mangoes, and 8 apples is twice the total cost of 1 orange, 2 mangoes, and 5 apples. This can be expressed algebraically as:
4O + 6M + 8A = 2(1O + 2M + 5A)
Simplifying the equation:
4O + 6M + 8A = 2O + 4M + 10A
Rearranging the terms to one side:
4O - 2O + 6M - 4M = 10A - 8A
2O + 2M = 2A
Dividing the entire equation by 2, the fundamental relationship between the costs is established:
O + M = A
Correct Option (C)
Both1and2
Statement 1: The total cost of 3 oranges, 5 mangoes, and 9 apples is equal to the total cost of 4 oranges, 6 mangoes, and 8 apples.
This statement can be written as an equation:
3O + 5M + 9A = 4O + 6M + 8A
To verify this statement, rearrange the terms:
9A - 8A = 4O - 3O + 6M - 5M
A = O + M
This derived equality (A = O + M) precisely matches the fundamental relationship established from the problem's initial condition. Therefore, Statement 1 is correct.
Statement 2: The total cost of one orange and one mango is equal to the cost of one apple.
This statement directly translates to the algebraic expression:
O + M = A
This is exactly the fundamental relationship derived from the problem's initial condition. Therefore, Statement 2 is correct.
Since both Statement 1 and Statement 2 are correct, option C is the correct answer.
Incorrect Options
Options A, B, and D are incorrect because both statements are valid and consistent with the information provided in the problem and the derived cost relationship (O + M = A).