Final answer:
To write an equation for making exactly $120 profit, use 8x + 5y = 120. To create an inequality for making more than $120 profit, use 8x + 5y > 120. There is no combination that would exactly result in $120 profit, but if she sells 10 necklaces, she can sell more than 8 bracelets to make more than $120 profit.
Step-by-step explanation:
To write an equation whose solution is the combination of necklaces and bracelets she could sell and make exactly $120 profit, we can let 'x' represent the number of necklaces and 'y' represent the number of bracelets. The equation would be:
8x + 5y = 120
To write an inequality whose solutions are the combinations of necklaces and bracelets she could sell and make more than $120 profit, we can use the greater than symbol. The inequality would be:
8x + 5y > 120
To find a combination of necklaces and bracelets that she could sell and make exactly $120 profit, we can substitute a value for 'x' and solve for 'y'. Let's assume she sells 14 necklaces (x = 14):
8(14) + 5y = 120
112 + 5y = 120
5y = 8
y = 1.6
Since 'y' represents the number of bracelets, we cannot have a fractional value for 'y'. Therefore, there is no combination that would result in exactly $120 profit.
To find a combination of necklaces and bracelets that she could sell and make more than $120 profit, we can try different values for 'x' and 'y'. For example:
Let's assume she sells 10 necklaces (x = 10):
8(10) + 5y > 120
80 + 5y > 120
5y > 40
y > 8
So, if she sells 10 necklaces, she can sell more than 8 bracelets to make more than $120 profit.