math
posted by mili on .
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