SOLUTION: In order to make a necklace, Alicia purchased a bag of 80 beads for a total of 39.00. Some of the beads were sterling silver and cost .40 each, and the rest were gemstone beads tha

Question 1163773: In order to make a necklace, Alicia purchased a bag of 80 beads for a total of 39.00. Some of the beads were sterling silver and cost .40 each, and the rest were gemstone beads that cost .65. How many of each type of bead were in the bag?
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
S=x and $ of S are 0.40x
G are 80-x and $G are 0.65(80-x) or 52-0.65x
That sum is 39.00
so 39.00=0.40x+52-0.65x
and -13.00=-0.25x
x=52 sterling silver for $20.80
80-x=28 Gemstone for $18.20
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

If a formal algebraic solution is not required, here is a quick and easy way to solve the problem with logical reasoning and some mental arithmetic.

80 beads all at .40 would cost 80(.40) = 32; 80 all at .65 would cost 80(.65) = 52.

Look at where the actual total cost lies between those two extremes. 39 is 7/20 of the way from 32 to 52. (32 to 52 is 20; 32 to 29 is 7; 39 is 7/20 of the way from 32 to 52.)

That means 7/20 of the beads were the higher priced beads.

7/20 of 80 is 7*4 = 28; 28 of the beads were the gemstone beads. The other 80-28=52 beads were the sterling silver beads.

ANSWER: 52 sterling silver, 28 gemstone.

CHECK: 52(.40)+28(.65) = 20.80+18.20 = 39

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