--------------------------------- Define x and y : --------------------------------- Let x be the number of large boxes. Let y be the number of smaller boxes.
--------------------------------- Construct equations : --------------------------------- x + y = 125 -------------------------- (1) 50x + 30y = 4850 ---------------- (2)
--------------------------------- From equation (1) : --------------------------------- x + y = 125 x = 125 - y
--------------------------------- Substitute x = 125 - y into (2) : --------------------------------- 50 (125 - y) + 30y = 4850 6250 - 50y + 30y = 4850 20y = 1400 y = 1400 ÷ 20 y = 70
--------------------------------- Sub y = 70 into equation 1 --------------------------------- x + y = 125 x + 70 = 125 x = 55
--------------------------------- Find the number of boxes : --------------------------------- Large box = x = 55 Small box = y = 70
--------------------------------------------------------------------------------------------------- Answer: There are 55 large boxes and 70 small boxes. ---------------------------------------------------------------------------------------------------
Let L and S represent the numbers of Large and Small boxes, respectively. .. L + S = 125 . . . . . . . . . . there are 125 boxes in all .. 50L + 30S = 4850 . . . . . total weight of all boxes is 4850 pounds
You can multiply the first equation by -30 and add that to the second. .. -30L -30S = -3750 Adding this to the second equation, we get .. (-30L +50L) +(-30S +30S) = (-3750 +4850) .. 20L = 1100 .. L = 55
and from the first equation ... .. 55 + S = 125 .. S = 70
The truck is carrying .. 55 large boxes .. 70 small boxes
_____ Subtraction and addition are basically the same thing. You just need to pay attention to the sign of the number.
Get rid of cos2x by dividing both the values. So Sin2x/cos2x +3cos2x/cos2x. Tan2x = 3 2x = -71.5 so x is -35.6 Use the quadrant method and add 360 twho the two values tou get.
