Question

a delivery truck is transporting boxes of two sizes large and small the large box weigh 45 pounds each and the small box weigh 35 pounds each there are 105 boxes in all if the truck is carrying a total of 4225 lb in boxes how many of each type of box is it carrying

Answer 1

the truck is carrying 55 large boxes and 50 small boxes

Step-by-step explanation:

Let the number of large boxes = x

Let the number of small boxes = y

Total boxes = 105

number of large boxes + number of small boxes = 105

x + y = 105 ...equation 1

pounds of x number of large boxes = x(45 pounds)

Pounds of y number of small boxes = y(35 pounds)

Total pounds of all boxes = 4225lb

pounds of x number of large boxes + pounds of y number of small boxes = 4225

x(45) + y(35) = 4225

45x + 35y = 4225 ...equation 2

Using substitution method:

From equation 1: x + y = 105

x = 105 - y

Substitute for x in equation 2:

45(105 - y) + 35y = 4225

4725 - 45y + 35y = 4225

4725 - 10y = 4225

4725 - 4225 = 10y

500 = 10y

y = 500/10

y = 50

substitute for y in equation 1:

x + 50 = 105

x = 105 - 50

x = 55

Hence, the truck is carrying 55 large boxes and 50 small boxes