System of Equations 2 — Heart of Algebra

Questions in this quiz (10)

1. A coffee roaster creates two premium blends. Blend X contains $$4$$ pounds of Kona beans and $$3$$ pounds of Ethiopian beans and sells for $$71$$. Blend Y contains $$5$$ pounds of Kona beans and $$2$$ pounds of Ethiopian beans and sells for $$74$$. What is the cost, in dollars, of $$1$$ pound of Kona beans?

   • $$11.43$$
   • $$8.50$$
   • $$10.75$$
   • $$9.65$$

2. At an office supply store, a customer purchased $$4$$ notebooks, $$3$$ pens, and $$2$$ markers for $$19.50$$ dollars. Another customer purchased $$2$$ notebooks, $$5$$ pens, and $$4$$ markers for $$21.50$$ dollars. If a marker costs $$2.00$$ dollars, what is the cost, in dollars, of one pen?

   • $$1.25$$
   • $$1.50$$
   • $$1.64$$
   • $$2.85$$

3. $$4x+5y=18$$$$12x+ky=54$$In the system of equations below, $$k$$ is a constant. If the system has infinitely many solutions, what is the value of $$k$$?

   • $$10$$
   • $$12$$
   • $$15$$
   • $$18$$

4. $$9x+4y=38$$$$5x-2y=2$$If the solution to the system is $$(x,y)$$, what is the value of $$2x+3y$$?

   • $$\frac{4}{9}$$
   • $$\frac{3}{4}$$
   • $$\frac{8}{9}$$
   • $$\frac{342}{19}$$

5. A school sold student tickets, adult tickets, and VIP tickets for a fundraising event. Student tickets cost $$12$$ each, adult tickets cost $$18$$ each, and VIP tickets cost $$30$$ each. A total of $$500$$ tickets were sold. Of these, $$80$$ were VIP tickets. The total revenue was $$8,520$$. If the number of adult tickets sold was $$40$$ more than the number of student tickets sold, how many student tickets were sold?

   • $$160$$
   • $$180$$
   • $$190$$
   • $$210$$

6. A customer purchases two types of coffee beans. Premium beans cost $$18$$ per pound, and standard beans cost $$11$$ per pound. The customer buys a total of $$20$$ pounds and spends $$297$$. How many pounds of premium beans were purchased?

   • $$9$$
   • $$11$$
   • $$13$$
   • $$15$$

7. $$(k-2)x+4y=12$$$$6x+(k+1)y=9$$In the system of equations below, $$k$$ is a constant. If the system has no solution, what is the value of $$k$$?

   • $$\frac{1+\sqrt{105}}{2}$$
   • $$\frac{2+\sqrt{10}}{5}$$
   • $$\sqrt{10}$$
   • $$\frac{2-\sqrt{105}}{4}$$

8. $$7x-5y=11$$ $$3x+2y=8$$If the solution to the system is $$(x,y)$$, what is the value of $$9x-4y$$?

   • $$\frac{45}{29}$$
   • $$\frac{81}{2}$$
   • $$\frac{466}{29}$$
   • $$\frac{465}{71}$$

9. $$3x+ky=24$$$$5x-4y=12$$Given the system of equations above, the solution $$(x,y)$$ satisfies $$2x+y=8.$$ What is the value of $$k$$?

   • $$\frac{8}{3}$$
   • $$4$$
   • $$\frac{45}{4}$$
   • $$6$$

10. A theater sells regular tickets for $$14$$ and premium tickets for $$22$$. On a certain night, $$420$$ tickets were sold for a total revenue of $$7,560$$. In addition, the number of premium tickets sold was $$60$$ fewer than twice the number of regular tickets sold. How many premium tickets were sold?

    • $$180$$
    • $$200$$
    • $$240$$
    • $$260$$