Solving Equations 5 — Heart of Algebra

Questions in this quiz (10)

1. The equation $$\frac{c(3x-1)}{2}+d=\frac{x+d}{4}$$ has no solution, where $$c$$ and $$d$$ are constants. The constant $$d$$ CANNOT be equal to the constant $$k$$. What is the value of $$c-k$$?

   • $$\frac{5}{18}$$
   • $$\frac{1}{18}$$
   • $$-\frac{1}{18}$$
   • $$-\frac{5}{18}$$

2. A father is currently $$28$$ years older than his son. Let $$x$$ be the son's current age, in years. In $$5$$ years, the father's age will be three times the son's age from $$10$$ years ago. Which of the following equations can be used to find the value of $$x$$?

   • $$x+33=3(x+10)$$
   • $$x+5=3(x-10)$$
   • $$x+33=3(x-10)$$
   • $$x+33=3x-10$$

3. In the equation $$\frac{4x+1}{x-3}=\frac{4x+9}{x-2},$$ the values of $$x$$ are restricted such that $$x\ne3$$ and $$x\ne2$$. If the solution to the equation is denoted by $$s$$, what is the value of $$8s+3$$?

   • 53

4. A warehouse receives a shipment of electronics. The first section contains $$\frac{2}{5}$$ of the total items. The second section contains $$\frac{1}{4}$$ of the remaining items after the first section is removed. The third section contains $$45$$ more items than the second section. If the third section contains $$120$$ items, what was the total number of items in the shipment?

   • 500

5. A chemist mixes Solution A, which is $$15\%$$ acid, with Solution B, which is $$80\%$$ acid. The chemist wants to create $$250$$ milliliters of a solution that is $$54\%$$ acid. How many milliliters of Solution A should be used?

   • $$100$$
   • $$125$$
   • $$150$$
   • $$175$$

6. A company plans to purchase a manufacturing machine. The total cost consists of the base price, a delivery fee of $$2,400$$ dollars, and an installation fee of $$1,600$$ dollars. The owner has $$18,000$$ dollars in savings and qualifies for a grant covering $$25\%$$ of the total cost. The remaining amount will be financed through a loan. If the required loan amount is $$42,000$$, what is the base price of the machine?

   • $$68,000$$
   • $$72,000$$
   • $$76,000$$
   • $$80,000$$

7. A factory produces two types of products, Type A and Type B. The production cost of Type A is $$18$$ dollars per unit, and the production cost of Type B is $$30$$ dollars per unit. On a certain day, the factory's total production cost was $$21,600$$ dollars. The number of Type B units produced was $$80$$ more than $$\frac{3}{4}$$ of the number of Type A units produced. How many Type A units were produced? (Express your answer as an integral)

   • 474

8. A specialty coffee shop sells two varieties of coffee beans: Kenyan AA and Sumatra Mandheling. A customer purchased $$3$$ pounds of Kenyan AA and $$2$$ pounds of Sumatra Mandheling for $$73$$ dollars. Another customer purchased $$2$$ pounds of Kenyan AA and $$5$$ pounds of Sumatra Mandheling for $$98$$ dollars. What is the total cost, in dollars, of $$4$$ pounds of Kenyan AA and $$3$$ pounds of Sumatra Mandheling?

   • $$96$$
   • $$102$$
   • $$110$$
   • $$117$$

9. An electrician charges a flat service fee of $$90$$ dollars. The first $$3$$ hours of labor are billed at $$75$$ dollars per hour. Any additional time is billed at $$55$$ dollars per hour. If a customer's bill totaled $$535$$ dollars, how many hours did the electrician work?

   • $$7$$
   • $$8$$
   • $$9$$
   • $$10$$

10. A manufacturing company produces two products, Product X and Product Y.The company also incurs a fixed daily operating cost of $$1,200$$ dollars. On a particular day, the company sold $$120$$ units of Product X. If the company wants to achieve a total daily profit of $$5,280$$, how many units of Product Y must be sold?

    • 159