11th grade math algebra 2 trig
posted by Nick .
you are buying beads and string to make a necklace. the string coast $1.50 a pack of 10 decorative beads costs $0.50 and a pack of 25 plain beads costs $0.75 you can only spend $7.00 and you need 150 beads you wish the necklace to be as decrative as possiable how many packs of each type of bead should you buy?

Your problem would be clearer if you placed periods at the end of each sentence, started each sentence with a capital letter, and added commas where needed. We could live without the commas but not the other two.

you are buying beads and string to make a necklace. The string coast $1.50; A pack of 10 decorative beads costs $0.50; And a pack of 25 plain beads costs $0.75. You can only spend $7.00 and you need 150 beads. You wish the necklace to be as decrative as possiable. How many packs of each type of bead should you buy?

Here is what I would do.
We need the string regardless. Therefore, 7.00  1.50 for the string leaves 5.50 for the two kinds of beads.
Let d = decorative beads. They cost 0.50 for a pack of 10 which makes them cost 0.05 (a nickel) each.
Let p = plain beads. They cost 0.75 for a pack of 25 or 0.03 (3 cents) each. Then set up two equations for the two unknowns.
=================
total beads = 150 so
d + p = 150
cost of beads = 5.50 so
0.05d + 0.03p = 5.50
Solve the two equations for d and p. Then divide them up into packets; i.e., total d beads divided by 10 = # packets and total p beads divided by 25 = # packets. Calculate the price of the packets to make sure the total is 5.50. Then, to make sure this is the best that can be done, take 1 pack of plain beads and replace with pack(s) of d beads and see if you can end up with 150 beads at a cost of 5.50. 
WHAT IS
X2+289 
simplify. Assume that no variable equals 0.
30y4power over 5y2power 
if you buy 3 sets of the decorative beads at .50 a piece and 5 sets of the plain beads at .75 a piece plus the string 1.50 that would give you a grand total of 6.75 and with a quarter left over and 5 beads that is more than what you need.

5 packs of decorative beads,
4 packs of plain beads
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