Question

Two mangoes, three grapes and four apples cost Rs. 15. Three mangoes, two grapes and one apple cost Rs. 10. I bought 3 Mangoes, 3 grapes and 3 apples. How much did I pay?

Answer 1

Hint: We can assume the cost of mangoes, grapes and apples and form equations to solve the problem. Make two equations based on the given data in the question and then manipulate so that we get the value of x + y + z. This value can then be multiplied by 3 to get the required value.

Complete step-by-step answer:
We proceed by first assigning a variable to the cost of mangoes, grapes and apples to be x, y and z rupees respectively.
Now we have,
Cost of two mangoes=Rs. 2x.
Cost of three grapes= Rs. 3y.
Cost of four apples= Rs. 4z.
The first sentence says that the cost of 2 mangoes, 3 grapes and 4 apples combined is Rs. 15.
Therefore, we can write 2x+3y+4z=15 …(i)
And we also have,
Cost of three mangoes=Rs. 3x.
Cost of two grapes= Rs. 2y.
Cost of one apple= Rs. z.
Therefore, we can write the second sentence as the following equation:
3x+2y+z=10 …(ii)
We need to calculate the cost of 3 mangoes, 3 apples and 3 grapes.
Therefore, we need to find solution of 3x+3y+3z by using the above two equations.
2x+3y+4z=15 …(i)
3x+2y+z=10 …(ii)
Adding equations (i) and (ii), we get 5x + 5y + 5z = 25.
We now divide both sides of the equation by 5 to get x + y + z = 5.
Multiplying both sides of the equation by 3, we get 3x + 3y + 3z = 15.
Thus, we get that the total cost of 3 mangoes, 3 apples and 3 grapes is Rs. 15.
Note: Here, we derived the value of x + y + z by manipulating the equations given and thus were able to find the required value even though the individual values of x, y and z were unknown to us. This is not always the case as, in most cases, we need 3 equations to get the values of x, y and z and then find the required value.