Making more money!

Question

Okay So I want to make money out of 130 dollars, A store is selling cool glasses for 30 bucks and another pawn shop is willing to buy these glasses for 50, and occasionally 65 if they are from the right series. I can only hold 26 of these glasses at a time and evey 8th glasses I sell are the ones worth 65. How many would it take to reach 9,999 dollars from doing these sales? dont worry about how glasses there are in the store lets say its unlimited.

Answer 1

You can only buy four to start: 4 * 30 = 120    130 - 120 = 10 left over

Sell for 50 each:  4 * 50 = 200       200 + 10 = 210                     Tally:   4

 

Buy seven:  7 * 30 = 210    0 left over

Sell six for 50, one for 65:  6 * 50 + 65 = 365                             Tally:   11

 

Buy twelve:  12 * 30 = 360        365 - 360 = 5 left over

Sell eleven for 50, one for 65:  11 * 50 + 65 = 615   615 + 5 = 620     Tally:   23

 

Buy twenty:  20 * 30 = 600       620 - 600 = 20 left over

Sell seventeen for 50, three for 65: 17 * 50 + 3 * 65 = 1045   1045 + 20 = 1065    Tally:  43

 

Now we have enough money to buy the max 26:  26 * 30 = 780   1065 - 780 = 285 left over

Sell 23 * 50 + 3 * 65 = 1345     1345 + 285 = 1630               Tally:  69

 

1630 - 780 = 850 left over

23 * 50 + 3 * 65 = 1345      1345 + 850 = 2195            Tally:  95

 

2195 - 780 = 1415 left over

22 * 50 + 4 * 65 = 1360      1360 + 1415 = 2775          Tally:  121

 

You can see the repetitive nature of this computation, best completed on a spread sheet. But the only reason to go through all this is if you need to keep track of how many transactions are involved. The question appears to be asking only how many pairs of glasses need to be moved.

 

If x is the total number of glasses moved, then we can write an equation for the profit based on the difference in purchases and sales prices. All of the glasses make at least 20 dollars profit. Every eighth pair makes an extra 15 dollars. Therefore:

 

Total = 130 + 20x + 15x/8

Total = 130 + 175x/8

 

9999 = 130 + 175x/8

9869 = 175x/8

78952 = 175x

451.15 = x

 

So 451 pairs of glasses would be just shy of 9999.

 

452 pairs of glasses would put you over.