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% pecans. The resultuing mixture is 82% pecans. How many pounds of nut mixture does Rina make?

Question

Mathematics

Zayden Moses

11 November, 16:45

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% pecans. The resultuing mixture is 82% pecans. How many pounds of nut mixture does Rina make?

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Morse · Answer 1

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