The average mass of 2 durians and 3 apples is 1.85kg. The average mass of 3 durians and 3 apples is 1.92kg. What is the mass of 1 durian?
Using the definition of "average", and A and D for the masses of each,
2D + 3A = 1.85 x 5 = 9.25
3D + 3A = 1.92 x 6 = 11.52
D = 2.27 kg
This leads to a very high mass for 1 apple-- over 1 kg. The numbers seem raqther phoney
yup, it is...thanks
To find the mass of 1 durian, we will use algebraic equations based on the given information.
Let's assume the mass of 1 durian is 'D' and the mass of 1 apple is 'A.'
From the first statement, we can form the equation:
2D + 3A = 1.85kg ---(1)
From the second statement, we can form a similar equation:
3D + 3A = 1.92kg ---(2)
Now, we have a system of two equations with two variables. We can solve these equations simultaneously to find the values of 'D' and 'A.'
To eliminate 'A' from the equations, we can multiply equation (1) by 3 and equation (2) by 2:
(3) * (2D + 3A) = (3) * (1.85kg)
(2) * (3D + 3A) = (2) * (1.92kg)
Simplifying these equations, we get:
6D + 9A = 5.55kg ---(3)
6D + 6A = 3.84kg ---(4)
Now, subtracting equation (4) from equation (3), we can eliminate 'D' and solve for 'A':
(6D + 9A) - (6D + 6A) = 5.55kg - 3.84kg
3A = 1.71kg
A = 1.71kg / 3
A = 0.57kg
Now, substitute the value of 'A' back into any of the original equations. Let's use equation (1):
2D + 3(0.57kg) = 1.85kg
2D + 1.71kg = 1.85kg
2D = 1.85kg - 1.71kg
2D = 0.14kg
D = 0.14kg / 2
D = 0.07kg
Therefore, the mass of 1 durian is 0.07kg.