Annna wants to buy her grandmother a gift. Anna decides to buy a piece of jewelry. At the store she sees that 1/2 of the jewelry is necklaces. 1/4 of the jewelry is pins. The rest of the jewelry is a total of 16 bracelets and rings. There are 3 times as many bracelets as rings. How many of each piece of jewelry does the store have for Anna to decide what to buy for her grandmother? If necklaces average $25, pins average $12, bracelsts average $8 and rings average $30,about how much inventory is in this jewelry store?
please explain steps along with answers
THANK YOU
HELP MATH - Gabrielle, Sunday, November 15, 2009 at 8:12pm
If you tell me what you've figured out on your own, I'll be happy to walk you through the rest of it! Here is what I did:
First I multied to find out how many braclets there were 16 X 3 = 48 bracelets 48 X $8 = 384
Then I converted 1/2 to 50 Next I converted 1/4 to 25. After that I added the cost of everthing individually.Finally I added the cost of everthing together.
My answer: 48 bracelets, 16 rings, 50 necklaces, and 25 pins. Inventory is
6,734.00
Let's look at this part:
" The rest of the jewelry is a total of 16 bracelets and rings. There are 3 times as many bracelets as rings "
let the number of rings be x
then the number of bracelets is 3x
3x + x = 16
4x = 16
x = 4
So we know there are 4 rings and 12 bracelets.
Now let the total number of jewelry be y
" At the store she sees that 1/2 of the jewelry is necklaces. 1/4 of the jewelry is pins. The rest of the jewelry is a total of 16 bracelets and rings "
y/2 + y/4 + 16 = y
multiply by 4
2y + y + 64 = 4y
y = 64
total number of jewelry is 64
Necklaces = y/2 = 32
Pins = y/4 = 16
bracelets = 12
rings = 4
inventory = $25(32) + $12(16) + $8(12) + $30(4) = $1208
thanks reiny.
To solve this problem, we need to break it down into smaller steps. Let's start by analyzing the information given.
According to the statement, 1/2 of the jewelry is necklaces. This means that if we have x pieces of jewelry, (1/2)x will be necklaces.
Similarly, 1/4 of the jewelry is pins. Therefore, (1/4)x will be pins.
The remaining jewelry consists of bracelets and rings and the total number of these is given as 16. Furthermore, we are told that there are 3 times as many bracelets as rings.
Let's suppose that the number of rings is y. In that case, the number of bracelets would be 3y, as stated in the problem. And the total number of bracelets and rings is given as 16, which can be written as y + 3y = 16.
Now we have two equations:
(1/2)x = necklaces
(1/4)x = pins
y + 3y = 16
To solve for x, y, and find the number of each type of jewelry, we need to rewrite the third equation and then solve the system of equations.
Looking at the second equation, we can multiply both sides by 4 to eliminate the fraction:
4 * (1/4)x = 4 * pins
x = 4 * pins
Substituting this into the first equation gives:
(1/2)(4*pins) = necklaces
2*pins = necklaces
Since we know that the total number of jewelry is 16, we can substitute the values we found into the equation:
y + 3y + 2*pins + 2*pins = 16
4*pins + 4y = 16
Substituting the value of x into this equation gives:
4*pins + 4y = 16
4*pins + 4*(2*pins) = 16
4*pins + 8*pins = 16
12*pins = 16
pins = 16/12
pins = 4/3
Since the number of pins cannot be a fraction, we need to adjust the values of the other variables accordingly. Multiplying both sides of the equation by 3 gives:
3 * pins = 4
Now, we can substitute this value back into the equation for finding y:
y + 3y = 16
4y = 16
y = 4
Knowing the values of pins and y, we can calculate the number of necklaces using the equation we derived earlier:
2*pins = necklaces
2 * 4 = necklaces
necklaces = 8
Finally, we can find the number of bracelets by substituting the value of y into the equation:
3y = bracelets
3 * 4 = bracelets
bracelets = 12
Therefore, the number of each piece of jewelry in the store is:
8 necklaces
4 pins
12 bracelets
4 rings
Now, let's calculate the total inventory value. We are given the average prices of each type of jewelry: $25 for necklaces, $12 for pins, $8 for bracelets, and $30 for rings.
The total inventory value can be calculated by multiplying the number of each type of jewelry by their respective average prices and summing them up:
Total inventory value = (8 * $25) + (4 * $12) + (12 * $8) + (4 * $30)
Total inventory value = $200 + $48 + $96 + $120
Total inventory value = $464
Therefore, the total inventory value in the jewelry store is $464.