Dr. Bob222 I am sorry for my improper use of grammar. (not intended in a smart alike way.)
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?
Answered below.
Let me know if I need to explain anything more.
5>4b+9>17
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To solve this problem, we need to find the number of packs of each type of bead needed to make a necklace with 150 beads while spending no more than $7.00 and maximizing the decorative nature of the necklace.
Let's assume you buy x packs of decorative beads and y packs of plain beads.
Each pack of decorative beads contains 10 beads, so the total number of decorative beads would be 10x.
Each pack of plain beads contains 25 beads, so the total number of plain beads would be 25y.
Now we can set up the equations based on the given information:
1. The total cost equation: 1.50 + 0.50x + 0.75y <= 7.00
This equation ensures that the total cost of the string and beads does not exceed $7.00.
2. The total number of beads equation: 10x + 25y = 150
This equation represents the requirement of having a total of 150 beads.
To solve this system of equations, we can use various methods such as substitution, elimination, or graphing. In this case, substitution is the simplest method.
First, let's solve the second equation for x:
10x = 150 - 25y
x = (150 - 25y) / 10
Now substitute this value of x into the first equation:
1.50 + 0.50[(150 - 25y) / 10] + 0.75y <= 7.00
Simplifying the equation:
1.50 + (0.05)(150 - 25y) + 0.75y <= 7.00
1.50 + 7.50 - 1.25y + 0.75y <= 7.00
9.00 - 0.50y <= 7.00
-0.50y <= -2.00
y >= 4
Since the number of packs cannot be negative, we can ignore the inequality and focus on the second equation:
10x + 25y = 150
Substituting the value of y as 4:
10x + 25(4) = 150
10x + 100 = 150
10x = 50
x = 5
So, you should buy 5 packs of decorative beads (50 beads) and 4 packs of plain beads (100 beads) to make a necklace with a total of 150 beads while spending no more than $7.00.