Carson is refilling his tires. Each tire can hold 500 cubic inches of air. Two of the tires are completely flat and empty. One tire is 40% full and the last tire is 70% full. If Carson injects 50 cubic inches of air with each pump, how many pumps will it take him to fill all the tires?
Thoughts? Step-by-step reasoning:
First, if the a full tire needs 500 cubic inches of air, then two empty tires need: 500 cubic inches / tire * 2 tires = 1000 cubic inches. Accordingly, the 40% - full tire needs 500 cubic inches * (100% - 40%). So, we find the 40% - full tire needs 500 cubic inches * (60%) = 300 cubic inches. And, the 70% - full tire needs 500 cubic inches * (100% - 70%). So, the 70% - full tire needs 500 cubic inches * (30%) = 150 cubic inches. Now add up the needs of all the tires to find the total number of cubic inches needed: 1000 cubic inches + 300 cubic inches + 150 cubic inches = 1450 cubic inches. Finally, if the pumps each hold 50 cubic inches, the total number of pumps needed is 1550 cubic inches / 50 cubic inches / pump = 29 pumps.
Thus, the answer is 29.