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

Question

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

Answer 1

Let's represent the cost of each bead in Bag A as 'a', in Bag B as 'b', and in Bag C as 'c'. We need to determine which bag of beads Jen should buy, considering that she does not want to use beads that cost more than $1 each.

From the given information, we can set up the following equations:

Equation 1: a / 100 = 18.25 / 100 beads per dollar
Simplified: a = 0.1825

Equation 2: b / 10 = 15.50 / 10 beads per dollar
Simplified: b = 1.55

Equation 3: c / 1000 = 12.00 / 1000 beads per dollar
Simplified: c = 0.012

Since Jen does not want to use beads that cost more than $1 each, we can eliminate Bag A as the cost of each bead in Bag A (0.1825) is greater than 1.

The cost of each bead in Bag B is $1.55, which also exceeds the limit of $1 set by Jen.

The cost of each bead in Bag C is $0.012, which is well within Jen's price range.

Therefore, Jen should buy Bag C, as the cost of each bead is below $1.

Answer 2

To determine which bag of beads Jen should buy, we need to compare the cost per bead of each bag and find the one that is less than or equal to $1.

Let's define:
BtA - the cost of beads per bead in Bag A
BtB - the cost of beads per bead in Bag B
BtC - the cost of beads per bead in Bag C

We can write the equations as follows:

BtA = 18.25 / 100
BtB = 15.50 / 10
BtC = 12.00 / 1000

Simplifying the equations, we get:

BtA = 0.1825
BtB = 1.55
BtC = 0.012

Now, we can compare the cost per bead of each bag:

BtA ≤ 1
0.1825 ≤ 1

BtB ≤ 1
1.55 ≤ 1 (not true)

BtC ≤ 1
0.012 ≤ 1

From the comparison, we can see that only Bag A and Bag C have costs per bead that are less than or equal to $1. Considering Bag B has a cost per bead of $1.55, it does not meet Jen's criteria.

Therefore, Jen should buy Bag A or Bag C, depending on her needs and preferences.

Answer 3

To determine which bag of beads Jen should buy, we need to compare the cost per bead for each bag with her maximum budget of $1 per bead.

Let's calculate the cost per bead for each bag:

For Bag A:
Cost = $18.25
Number of beads = 100
Cost per bead = $18.25 / 100 = $0.1825 per bead

For Bag B:
Cost = $15.50
Number of beads = 10
Cost per bead = $15.50 / 10 = $1.55 per bead

For Bag C:
Cost = $12.00
Number of beads = 1000
Cost per bead = $12.00 / 1000 = $0.012 per bead

Now, let's compare the cost per bead of each bag with Jen's budget of $1 per bead:

For Bag A: $0.1825 per bead < $1 per bead (within budget)
For Bag B: $1.55 per bead > $1 per bead (over budget)
For Bag C: $0.012 per bead < $1 per bead (within budget)

Based on the calculations above, Bag A and Bag C are both within Jen's budget of $1 per bead. However, Bag C offers a much lower cost per bead compared to Bag A.

Therefore, Jen should buy Bag C because it provides more beads for a lower cost per bead.

Equations to justify this reasoning:

Cost per bead for each bag:
Bag A: Cost per bead = Cost of Bag A / Number of beads in Bag A
Bag B: Cost per bead = Cost of Bag B / Number of beads in Bag B
Bag C: Cost per bead = Cost of Bag C / Number of beads in Bag C

Comparison with Jen's budget:
If Cost per bead < $1 per bead -> Within budget
If Cost per bead > $1 per bead -> Over budget

Comparison of Bags:
If Bag A within budget
And Bag B over budget
And Bag C within budget
-> Choose the bag with the lowest cost per bead (i.e., Bag C)

Hope this helps!