a basket of with 12 apples has a mass of 3105 grams. the same basket with 7 apples has a mass of 1,980 grams. each apple has the same mass. what is the mass of the basket?
a = mass of one aple
b = mass of basket
1 basket :
12 a + b = 3105 Subtract 12 a to both sides
12 a + b - 12 b = 3105 - 12 a
b = 3105 - 12 a
2 basket :
7 a + b = 1980
7 a + 3105 - 12 a = 1980
- 5 a + 3105 = 1980 Subtract 3105 to both sides
- 5 a + 3105 - 3105 = 1980 - 3105
- 5 a = -1125 Divide both sides by - 5
- 5 a / - 5 = - 1125 / - 5
a = 225 grams
b = 3105 - 12 a
b = 3105 - 12 * 225
b = 3105 - 2700
b = 405 grams
Proof :
12 a + b = 3105
12 * 225 + 405 = 3105
2700 + 405 = 3105
3105 = 3105
7 a + b = 1980
7 * 225 + 405 = 1980
1575 + 405 = 1980
1980 = 1980
1 basket :
12 a + b = 3105 Subtract 12 a to both sides
12 a + b - 12 a = 3105 - 12 a
b = 3105 - 12 a
To find the mass of the basket, we need to subtract the mass of the apples from the total mass of the basket in both scenarios.
Let's denote the mass of the basket as "b" and the mass of each apple as "a".
From the given information, we have two equations:
Equation 1: 12a + b = 3105 (mass of the basket with 12 apples)
Equation 2: 7a + b = 1980 (mass of the basket with 7 apples)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of elimination:
1. Multiply both sides of Equation 2 by -1: -7a - b = -1980
2. Add Equation 1 to the modified Equation 2:
(12a + b) + (-7a - b) = 3105 + (-1980)
5a = 1125
3. Divide both sides of the equation by 5:
a = 225
Now that we have the value of "a," we can substitute it into either equation to solve for the mass of the basket, "b."
Let's use Equation 1:
12(225) + b = 3105
2700 + b = 3105
b = 4105 - 2700
b = 405
Therefore, the mass of the basket is 405 grams.