A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?

9514 1404 393

  11 cartons

Step-by-step explanation:

By shipping all 96 boxes as large boxes, the merchant will have shipped

  (96 boxes)/(8 boxes/large carton) = 12 large cartons*

He can ship as many boxes in 4 cartons of small boxes as in 5 cartons of large boxes. So trading 5 cartons of large boxes for 4 cartons of small boxes, he can reduce the number of cartons shipped by 1.

The merchant shipped 11 cartons:

  7 cartons of large boxes (56 large boxes)

  4 cartons of small boxes (40 small boxes)

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Any further such trade would reduce the number of large boxes to fewer than small boxes, violating the problem constraint.

* In this expression, we use the term "large carton" to mean "carton of large boxes".

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3