Elena is considering buying bracelets and necklaces as gifts for her friends. Bracelets cost \$3, and necklaces cost \$5. She can spend no more than \$30 on the gifts. Elena needs at least 7 gift items.

This graph represents the inequality \(3b+5n \leq30\), which describes the cost constraint in this situation.

Let \(b\) represent the number of bracelets and \(n\) the number of necklaces.

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1. Write an inequality that represents the number of gift items that Elena needs.
2. On the same coordinate plane, graph the solution set to the inequality you wrote.
3. Use the graphs to find at least two possible combinations of bracelets and necklaces that Elena could buy.
4. Explain how the graphs show that the combination of 2 bracelets and 5 necklaces meets one constraint in the situation but not the other constraint.

A gardener is buying some topsoil and compost to fill his garden. His budget is \$70. Topsoil costs \$1.89 per cubic foot, and compost costs \$4.59 per cubic foot.

Select all statements or representations that correctly describe the gardener's constraints in this situation. Let \(t\) represent the cubic feet of topsoil and \(c\) the cubic feet of compost.

Priya writes the equation \(y=\text- \frac12 x - 7\). Write an equation that has:

1. exactly one solution in common with Priya's equation
2. no solutions in common with Priya's equation
3. infinitely many solutions in common with Priya's equation, but looks different than hers

Here is a riddle:

• The sum of two numbers is less than 10.
• If we subtract the second number from the first, the difference is greater than 3.

Write a system of inequalities that represents this situation. Let \(f\) represent the first number and \(s\) represent the second number.