A basket with 12 apples has mass of 3105 grams. The same basket w 7 apples has a mass of 1980 grams. Each apple has same mass. What is mass of the basket
b + 12a = 3105
b + 7a = 1980
5a = 1125
a = 225
b = 405
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To find the mass of the basket, we need to first determine the mass of each individual apple.
We know that a basket with 12 apples has a total mass of 3105 grams. Therefore, the total mass of the apples in the basket can be found by subtracting the mass of the basket itself from the total mass.
Mass of 12 apples = 3105 grams - mass of basket
Similarly, for the basket with 7 apples, the total mass of the apples can be found by subtracting the mass of the basket from the total mass.
Mass of 7 apples = 1980 grams - mass of basket
Since it is mentioned that each apple has the same mass, we can divide the mass of the apples by the number of apples to find the mass of each individual apple.
Now we can set up two equations to solve for the mass of the basket. Let's call the mass of the basket "x".
Equation 1: 3105 grams - x = 12 apples * mass of each apple
Equation 2: 1980 grams - x = 7 apples * mass of each apple
To solve this system of equations, we can use the method of substitution. Rearrange Equation 1 to solve for mass of each apple:
Mass of each apple = (3105 grams - x) / 12
Now substitute this expression for the mass of each apple into Equation 2:
1980 grams - x = 7 * [(3105 grams - x) / 12]
Simplify the equation:
1980 grams - x = (7/12) * (3105 grams - x)
Multiply both sides of the equation by 12 to eliminate the fraction:
23760 grams - 12x = 7 * (3105 grams - x)
Distribute on the right side:
23760 grams - 12x = 21735 grams - 7x
Combine like terms:
5x = 2015 grams
Divide both sides of the equation by 5:
x = 403 grams
Therefore, the mass of the basket is 403 grams.