Inequalities 2 — Heart of Algebra

Questions in this quiz (10)

1. A community garden can grow tomatoes and peppers. Let $$t$$ represent the number of tomato plants and $$p$$ represent the number of pepper plants. The garden can hold at most $$900$$ plants total. Additionally, the number of tomato plants must be at least $$150$$ more than twice the number of pepper plants. Which of the following ordered pairs $$(t,p)$$ could represent a possible arrangement of plants in the garden?

   • $$(500,150)$$
   • $$(450,200)$$
   • $$(400,180)$$
   • $$(300,250)$$

2. A student council is selling notebooks and water bottles. Each notebook costs $$4.50$$, and each water bottle costs $$7.00$$. The council wants to raise at least $$250$$. If $$x$$ represents the number of notebooks sold and $$y$$ represents the number of water bottles sold, which inequality represents the fundraising goal?

   • $$4.5x+7y\ge250$$
   • $$4.5x+7y\le250$$
   • $$7x+4.5y\ge250$$
   • $$4.5x+7y=250$$

3. A factory produces two products, Product A and Product B. Each unit of Product A requires $$4$$ hours of labor and $$6$$ units of raw material. Each unit of Product B requires $$5$$ hours of labor and $$8$$ units of raw material. The factory has at most $$180$$ labor hours and $$300$$ units of raw material available each day. If the factory produces $$12$$ units of Product B, what is the maximum number of units of Product A that can be produced?

   • $$44$$
   • $$54$$
   • $$30$$
   • $$64$$

4. $$y\le-2x+12$$$$y$$ > $$3x-5$$Which of the following ordered pairs $$(x,y)$$ is a solution to the system of inequalities shown?

   • $$(2,3)$$
   • $$(3,5)$$
   • $$(1,-1)$$
   • $$(4,4)$$

5. A bakery sells cupcakes for $$3.50$$ each and brownies for $$4.25$$ each. A customer plans to buy some of each item. The total amount spent must be at least $$45$$ and no more than $$70$$. Let $$c$$ represent the number of cupcakes and $$b$$ represent the number of brownies purchased. Which system of inequalities represents this situation?

   • $$3.5c+4.25b\ge45$$ and $$3.5c+4.25b\le70$$
   • $$3.5c+4.25b\le45$$ and $$3.5c+4.25b\ge70$$
   • $$3.5c+4.25b>45$$ and $$3.5c+4.25b>70$$
   • $$3.5c+4.25b\ge45$$ and $$3.5c+4.25b\ge70$$

6. The cost of a streaming subscription, $$C$$ dollars, is modeled by $$C=3m+8,$$ where $$m$$ is the number of months subscribed. A customer wants to spend at least $$35$$ but no more than $$65$$. Which of the following inequalities represents the possible values of $$m$$?

   • $$9\le m\le19$$
   • $$7\le m\le19$$
   • $$8\le m\le18$$
   • $$10\le m\le20$$

7. A student is purchasing folders and notebooks. Each folder costs $$2.50$$ and each notebook costs $$4.00$$. The student must buy at least $$18$$ items in total, and the total cost must not exceed $$55$$. What is the maximum number of notebooks the student can buy?

   • $$6$$
   • $$9$$
   • $$10$$
   • $$11$$

8. A school club is selling plain hoodies for $$18$$ each and custom hoodies for $$28$$ each. They need to sell at least $$25$$ hoodies in total. If their goal is to raise at least $$600$$, what is the minimum number of custom hoodies they must sell?

   • $$10$$
   • $$12$$
   • $$14$$
   • $$15$$

9. A bakery has a daily budget of $$540$$ to produce cookies and croissants. The cost to make one cookie is $$2.50$$ and the cost to make one croissant is $$4.00$$. The bakery must produce at least $$180$$ items total each day. Additionally, the number of cookies produced must be at least twice the number of croissants produced. What is the maximum number of croissants the bakery can produce in one day?

   • $$45$$
   • $$54$$
   • $$60$$
   • $$72$$

10. For what values of the constant $$k$$ does the inequality $$3x-k$$ < $$2x+5$$ have only negative integer solutions for $$x$$?

    • $$k\le-5$$
    • $$k$$ < $$-5$$
    • $$k\le-6$$
    • $$k$$ < $$-4$$