Four apples and six oranges weigh 61. Six apples and four oranges weigh 59 ounces. What is thee weight of one apple and one orange together.
Three ducks and two ducklings weigh 32kg. Four ducks and three ducklings weigh 44kg. All ducks weigh the same and all ducklings weigh the same. What is the weigh of two ducks and one ducklings?
If apples weigh x and oranges weigh y, then you have
4x+6y = 61
6x+4y = 59
so, 10x+10y = 120
x+y = 12
If ducks weigh x and ducklings weigh y, then
2x+2y = 32
4x+3y = 44
subtract the top from the bottom
2x+y = 12
To solve this problem, we can set up a system of equations.
Let's assume the weight of one apple is A ounces, and the weight of one orange is O ounces.
From the given information, we can write the following equations:
Equation 1: 4A + 6O = 61 (Four apples and six oranges weigh 61 ounces)
Equation 2: 6A + 4O = 59 (Six apples and four oranges weigh 59 ounces)
To find the weight of one apple and one orange together, we need to solve for the values of A and O.
There are multiple ways to solve this system of equations, but one common method is to use the method of substitution.
Step 1: Solve Equation 1 for A:
4A + 6O = 61
4A = 61 - 6O
A = (61 - 6O) / 4
Step 2: Substitute the value of A in Equation 2:
6A + 4O = 59
6((61 - 6O) / 4) + 4O = 59
(366 - 36O) / 4 + 4O = 59
366 - 36O + 16O = 236
366 - 20O = 236
-20O = 236 - 366
-20O = -130
O = -130 / -20
O = 6.5
Step 3: Substitute the value of O back into Equation 1 to solve for A:
4A + 6(6.5) = 61
4A + 39 = 61
4A = 61 - 39
4A = 22
A = 22 / 4
A = 5.5
Therefore, the weight of one apple and one orange together is 5.5 + 6.5 = 12 ounces.