Question

There are nuts in three boxes. In the first box, there are 6 fewer pounds of nuts than in the other two boxes combined. In the second box, there are 10 fewer pounds of nuts than in the other two boxes combined. How many pounds of nuts are there in the third box?

Answer 1

8 pounds

Explanation:

Let a, b, c represent the number of pounds of nuts in the first, second, and third boxes, respectively. We can write the equations ...

a = b +c -6 . . . . . first box has 6# fewer than the total of the others

b = a +c -10 . . . . second box has 10# fewer than the total of the others

Substituting the second equation into the first, we find ...

a = (a +c -10) +c -6

0 = 2c -16 . . . . subtract a

0 = c -8 . . . . . . divide by 2

8 = c . . . . . . . . . add 8

There are 8 pounds of nuts in the third box.