Thread: Delivery

A delivery agent delivers goods to four stores and then returns to the warehouse. The driver delivers 1/4 of the load to the 1st store, then 1/2 of the remainder at the next store, then 1/4 of the remainder at the 3rd store and 1/3 of what is left to the 4th store. The agent has 480 units of goods to go back to the warehouse. How many units of goods did he deliver?

Let x = total number of goods initially with the driver before distributions.

"The driver delivers 1/4 of the load to the 1st store,..."
Ist store receives (1/4)x = x/4
Remaining load = x -x/4 = (3/4)x = 3x/4

"... then 1/2 of the remainder at the next store,..."
2nd store receives (1/2)(3x/4) = 3x/8
Remaining load = 3x/4 -3x/8 = (2*3x -3x)/8 = 3x/8

"... then 1/4 of the remainder at the 3rd store..."
3rd store receives (1/4)(3x/8) = 3x/32
Remaining load = 3x/8 -3x/32 = (4*3x -3x)/32 = 9x/32

"... and 1/3 of what is left to the 4th store."
4th store receives (1/3)(9x/32) = 3x/32
Remaining load = 9x/32 -3x/32 = 6x/32

"The agent has 480 units of goods to go back to the warehouse."
That means 6x/32 = 480, so,
6x = 480*32
x = (480*32)/6
x = 80*32
x = 2560

"How many units of goods did he deliver?"
He has 2560 initially, then he has 480 returned, so,
2560 -480 = 2080 delivered. -----answer.

Check:
1st store, x/4 = 2560/4 = 640 received
2nd store, 3x/8 = 3*2560/8 = 960
3rd store, 3x/32 = 3*2560/32 = 240
4th store, 3x/32 also = 240 also
---------
Total = 640+960+240+240 = 2080 ----it checks, so, OK.

Thanks very much ticbol!