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 $18.25, Bag B. 10 $15.50, Bag C. $12.00. Which bag of beads should Jen buy? Write equations to justify your reasoning
Jen should choose Bag B, which costs $15.50 for 10 beads.
To justify this choice with an equation, we can compare the cost per bead for each bag.
For Bag A:
Cost per bead = $18.25 / 100 beads
Cost per bead = $0.1825
For Bag B:
Cost per bead = $15.50 / 10 beads
Cost per bead = $1.55
For Bag C:
Cost per bead = $12.00 / 1 bead
Cost per bead = $12.00
Since Jen does not want to use beads that cost more than $1 each, she should choose Bag B, as it has a cost per bead of $1.55.
To determine which bag of beads Jen should buy, we need to compare the price per bead for each bag.
Let's calculate the price per bead for each bag using the given information:
For Bag A:
Price = $18.25
Number of beads = 100
Price per bead = Price / Number of beads = $18.25 / 100
For Bag B:
Price = $15.50
Number of beads = 10
Price per bead = Price / Number of beads = $15.50 / 10
For Bag C:
Price = $12.00
Number of beads = 1
Price per bead = Price / Number of beads = $12.00 / 1
Now we can compare the price per bead for each bag.
For Bag A:
Price per bead = $18.25 / 100 = $0.1825
For Bag B:
Price per bead = $15.50 / 10 = $1.55
For Bag C:
Price per bead = $12.00 / 1 = $12.00
Since Jen does not want to use beads that cost more than $1 each, Bag B is the most expensive and should be eliminated.
Comparing Bag A and Bag C, Bag C is cheaper as the price per bead is $12.00 in Bag C compared to $0.1825 in Bag A.
Therefore, Jen should buy Bag C.
Equations:
Price per bead for Bag A = $18.25 / 100
Price per bead for Bag B = $15.50 / 10
Price per bead for Bag C = $12.00 / 1
To determine which bag of beads Jen should buy, we need to compare the prices of the bags and check if they meet Jen's requirement of not exceeding $1 per bead.
Let's write down the equations to justify our reasoning:
Let x be the number of beads in Bag A, y be the number of beads in Bag B, and z be the number of beads in Bag C.
The cost of Bag A is given as $18.25, so the cost per bead can be calculated as:
Cost per bead in Bag A = $18.25 / x
The cost of Bag B is given as $15.50, so the cost per bead can be calculated as:
Cost per bead in Bag B = $15.50 / y
The cost of Bag C is given as $12.00, so the cost per bead can be calculated as:
Cost per bead in Bag C = $12.00 / z
Jen does not want to use beads that cost more than $1 each, so we can write the following inequalities:
Cost per bead in Bag A ≤ $1 ---> $18.25 / x ≤ 1 ---> 18.25 ≤ x
Cost per bead in Bag B ≤ $1 ---> $15.50 / y ≤ 1 ---> 15.50 ≤ y
Cost per bead in Bag C ≤ $1 ---> $12.00 / z ≤ 1 ---> 12.00 ≤ z
To determine which bag of beads Jen should buy, we need to find the bag with the lowest cost per bead that satisfies the inequality.
Therefore, we can compare the values of x, y, and z to see which bag satisfies its respective inequality and has the lowest cost per bead.
By comparing the given prices, Bag C has the lowest price at $12.00. Since its cost per bead is less than or equal to $1, Bag C is the best option for Jen to buy.
So, Jen should buy Bag C.