Jen makes beaded jewelry to sell at art fairs. The price of the bags she can buy are shown below. Jen does not want to use beads that cost more than $1 each. Bag A. 100 beads for $18.25, Bag B. 10 beads for $15.50, Bag C.1000 beads for $12.00. Which bag of beads should Jen buy? Write equations to justify your reasoning
Let's denote the cost of each bead from Bag A as 'a', from Bag B as 'b', and from Bag C as 'c'.
From Bag A, we can write the equation:
100a = $18.25
From Bag B, we can write the equation:
10b = $15.50
From Bag C, we can write the equation:
1000c = $12.00
We can divide both sides of the equations by the number of beads to find the cost per bead:
a = $18.25 / 100 = $0.1825 (rounded to 4 decimal places)
b = $15.50 / 10 = $1.55
c = $12.00 / 1000 = $0.012
Since Jen does not want to use beads that cost more than $1 each, she should not buy beads from Bag B (since it costs $1.55 per bead).
The cost of beads from Bag A is $0.1825 per bead, which is less than $1, so she could buy beads from Bag A.
The cost of beads from Bag C is $0.012 per bead, which is also less than $1, so she could buy beads from Bag C as well.
In conclusion, Jen should buy beads from both Bags A and C.
To determine which bag of beads Jen should buy, we need to compare the cost per bead of each bag and choose the one that falls within her budget.
Let's write the equations to calculate the cost per bead for each bag:
For Bag A: Let x be the cost per bead in dollars.
We know that the bag has 100 beads for $18.25, so we can write the equation:
18.25/100 = x
For Bag B: Let y be the cost per bead in dollars.
We know that the bag has 10 beads for $15.50, so we can write the equation:
15.50/10 = y
For Bag C: Let z be the cost per bead in dollars.
We know that the bag has 1000 beads for $12.00, so we can write the equation:
12.00/1000 = z
Now, let's solve each equation to find the cost per bead (x, y, z).
For Bag A:
18.25/100 = x
0.1825 = x
For Bag B:
15.50/10 = y
1.55 = y
For Bag C:
12.00/1000 = z
0.012 = z
Since Jen does not want to use beads that cost more than $1 each, we need to compare the cost per bead (x, y, z) to $1. If any of the costs per bead exceed $1, then Jen should not buy that bag.
The cost per bead for Bag A (x) is 0.1825, which is less than $1.
The cost per bead for Bag B (y) is 1.55, which is more than $1.
The cost per bead for Bag C (z) is 0.012, which is less than $1.
Based on our calculations, Jen should buy Bag A, as it has the lowest cost per bead that falls within her budget.
To determine which bag of beads Jen should buy, we need to compare the prices for each bag and consider her requirement of not wanting to use beads that cost more than $1 each.
Let's assign variables to each bag:
Let A be Bag A (100 beads for $18.25)
Let B be Bag B (10 beads for $15.50)
Let C be Bag C (1000 beads for $12.00)
Now, let's write equations to compare the prices per bead for each bag:
For Bag A:
Cost per bead in Bag A = Price of Bag A / Number of Beads in Bag A
Cost per bead in Bag A = $18.25 / 100
For Bag B:
Cost per bead in Bag B = Price of Bag B / Number of Beads in Bag B
Cost per bead in Bag B = $15.50 / 10
For Bag C:
Cost per bead in Bag C = Price of Bag C / Number of Beads in Bag C
Cost per bead in Bag C = $12.00 / 1000
Now, let's compute the cost per bead for each bag:
Cost per bead in Bag A = $0.1825
Cost per bead in Bag B = $1.55
Cost per bead in Bag C = $0.012
Since Jen does not want to use beads that cost more than $1 each, she should NOT buy Bag B because its cost per bead is $1.55, which exceeds her limit.
Therefore, Jen should buy Bag A or Bag C, as they both have costs per bead lower than $1.