Rina is making a nut mixture to sell at the local farmers' market. She mixes 6 pounds of pecans with a nut mixture that is 70% p ecans. The resultuing mixture is 82% pecans. How many pounds of nut mixture does Rina make?
1 answer:
So the best way to do these is concentration1 (%) × volume1 = concentration2 × volume2 Or C1V1 + C2V2 = C3V3, where C1 = 100% (bc ALL pecans), V1 = 6 lbs, C2 = 70%, C3 = 82%: 100%×6 + 70%×v2 = 82%×(6+v2) 100%=1.00, 70%=.7, 82%=.82 note: if none is poured out then v3 = v1+v2 6 + .7v2 = .82 (6+v2) 6 + .7v2 = 4.92 + .82v2 6 + .7v2 -.7v2 = 4.92 + .82v2 -.7v2 6 = 4.92 + .12v2 6-4.92 = 4.92-4.92 + .12v2 1.08 = .12v2 .12v2/.12 = 1.08/.12 v2 = 9 lbs that's only v2!!! For the final poundage, we need v3: v3 = 6 + v2 = 6 + 9 = 15 lbs
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