The cost of 3 bananas 4 apples and 6 mangoes is rs.29 and the cost of 2 bananas 6 apples and 3 mangoes is rs.23.what is the cost of 7 bananas 16 apples and 12 mangoes???
Why we multiply 2 with second equation
3b+4a+6m = 29
2b+6a+3m = 23
multiply the 2nd equation by 2, then add the two equations.
Thank for it
To find the cost of 7 bananas, 16 apples, and 12 mangoes, we need to determine the cost of each individual fruit first.
Let's break down the given information:
1. "The cost of 3 bananas, 4 apples, and 6 mangoes is Rs. 29"
2. "The cost of 2 bananas, 6 apples, and 3 mangoes is Rs. 23"
From the given information, we can create two equations to solve for the individual fruit costs:
Equation 1: 3B + 4A + 6M = 29
Equation 2: 2B + 6A + 3M = 23
Now, let's solve these two equations to find the cost of each fruit.
Multiply Equation 1 by 2 and Equation 2 by 3, so that the coefficients of B are the same:
6B + 8A + 12M = 58
6B + 18A + 9M = 69
Now, subtract Equation 2 from Equation 1:
(6B + 8A + 12M) - (6B + 18A + 9M) = 58 - 69
-10A + 3M = -11
Next, to eliminate M from the equation, multiply Equation 2 by 4 and Equation 1 by 3:
12B + 16A + 24M = 116
9B + 27A + 13.5M = 103.5
Subtract Equation 1 from Equation 2:
(9B + 27A + 13.5M) - (12B + 16A + 24M) = 103.5 - 116
-3B + 11A - 10.5M = -12.5
Now we have a new equation:
-10A + 3M = -11
-3B + 11A - 10.5M = -12.5
Solve these two equations to find the values of A (apple cost) and M (mango cost).
Multiplying the first equation by 3 and the second equation by 10, we get:
-30A + 9M = -33
-30B + 110A - 105M = -125
Adding these two equations together, we get:
-30B + 110A - 105M + (-30A + 9M) = -125 + (-33)
-30B + 80A - 96M = -158
Simplifying the above equation, we get:
-30B + 80A - 96M = -158
Now, we have three equations:
-10A + 3M = -11
-3B + 11A - 10.5M = -12.5
-30B + 80A - 96M = -158
Solving these equations simultaneously will give us the values of A, B, and M.
Once we have the values of A (apple cost), B (banana cost), and M (mango cost), we can calculate the cost of 7 bananas, 16 apples, and 12 mangoes by multiplying the respective quantities with their corresponding costs and adding them together:
Cost of 7 bananas = 7 * B
Cost of 16 apples = 16 * A
Cost of 12 mangoes = 12 * M
Finally, add the costs together to find the total cost of 7 bananas, 16 apples, and 12 mangoes:
Total cost = (7 * B) + (16 * A) + (12 * M)