Mary is selling her crafts to earn money. She sells her bracelets for $6 and her necklaces for $10. Her goal is to make at least $120 in sales. Let x = the number of bracelets she sells. Let y = the number of necklaces she sells. Which of the following represents three possible solutions to the problem?
Are (5,9), (10,6), and (15,3) three possible solutions??
Thank you!!
yes.
To determine if (5,9), (10,6), and (15,3) are three possible solutions, we can evaluate each solution and check if it satisfies the given conditions.
Let's start with the first solution, (5,9):
- Let x = 5 (number of bracelets sold)
- Let y = 9 (number of necklaces sold)
Now, let's calculate Mary's sales:
- Selling 5 bracelets would earn 5 * $6 = $30
- Selling 9 necklaces would earn 9 * $10 = $90
- Total sales: $30 + $90 = $120
The first solution (5,9) satisfies the goal of making at least $120 in sales.
Next, let's evaluate the second solution, (10,6):
- Let x = 10 (number of bracelets sold)
- Let y = 6 (number of necklaces sold)
Sales calculation:
- Selling 10 bracelets would earn 10 * $6 = $60
- Selling 6 necklaces would earn 6 * $10 = $60
- Total sales: $60 + $60 = $120
The second solution (10,6) also satisfies the goal of making at least $120 in sales.
Finally, let's evaluate the third solution, (15,3):
- Let x = 15 (number of bracelets sold)
- Let y = 3 (number of necklaces sold)
Sales calculation:
- Selling 15 bracelets would earn 15 * $6 = $90
- Selling 3 necklaces would earn 3 * $10 = $30
- Total sales: $90 + $30 = $120
The third solution (15,3) satisfies the goal of making at least $120 in sales.
Therefore, all three solutions, (5,9), (10,6), and (15,3), are valid solutions to the problem.
To determine if (5,9), (10,6), and (15,3) are three possible solutions, we can plug the values of x and y into the equations and see if they satisfy the conditions.
Let's calculate the earnings for each solution:
For the first solution, (x,y) = (5,9)
Earnings from bracelets = 5 * $6 = $30
Earnings from necklaces = 9 * $10 = $90
Total earnings = $30 + $90 = $120
For the second solution, (x,y) = (10,6)
Earnings from bracelets = 10 * $6 = $60
Earnings from necklaces = 6 * $10 = $60
Total earnings = $60 + $60 = $120
For the third solution, (x,y) = (15,3)
Earnings from bracelets = 15 * $6 = $90
Earnings from necklaces = 3 * $10 = $30
Total earnings = $90 + $30 = $120
Therefore, all three solutions satisfy the condition of making at least $120 in sales. Hence, (5,9), (10,6), and (15,3) are three possible solutions to the problem.