Solving Equations 3 — Heart of Algebra

Questions in this quiz (10)

1. A theater sold premium tickets for $$18$$ dollars each and standard tickets for $$11$$ dollars each. The total revenue from ticket sales for one performance was $$2,145$$. Which equation represents the relationship between $$p$$, the number of premium tickets sold, and $$s$$, the number of standard tickets sold?

   • $$18p+11s=2145$$
   • $$11p+18s=2145$$
   • $$p+s=2145$$
   • $$29(p+s)=2145$$

2. A delivery company uses a truck that can carry a maximum total weight of $$2,400$$ kilograms. The truck is loaded with $$x$$ medium crates, each weighing $$18$$ kilograms, and $$y$$ large crates, each weighing $$32$$ kilograms. The equation $$18x+32y=2400$$ models the maximum load. Which of the following best describes the number $$32$$ in this context?

   • The number of large crates
   • The weight, in kilograms, of one large crate
   • The total weight of all large crates
   • The maximum weight the truck can carry

3. If $$5(2x-3)-4x=3x+11,$$ what is the value of $$x$$?

   • $$\frac{2}{3}$$
   • $$\frac{26}{3}$$
   • $$\frac{4}{3}$$
   • $$\frac{11}{3}$$

4. A sporting goods store sells basketballs for $$28$$ dollars each and soccer balls for $$22$$ dollars each. On a certain day, total sales from these items were $$1,232$$. Which equation represents the possible numbers of basketballs, $$b$$, and soccer balls, $$s$$, sold that day?

   • $$28b+22s=1232$$
   • $$22b+28s=1232$$
   • $$b+s=1232$$
   • $$50(b+s)=1232$$

5. A fruit stand sells peaches for $$2.40$$ dollars per pound and plums for $$1.80$$ dollars per pound. A customer buys a total of $$12$$ pounds of fruit consisting only of peaches and plums. If the total cost is $$25.20$$, how many pounds of peaches were purchased?

   • $$4$$
   • $$6$$
   • $$8$$
   • $$10$$

6. A specialty tea shop sells two blends: Mountain Blend and Valley Blend. Last week, total revenue from these two teas was $$5,760$$. The equation $$24m+18v=5760$$ represents the situation, where $$m$$ is the number of pounds of Mountain Blend sold and $$v$$ is the number of pounds of Valley Blend sold. According to the equation, which of the following represents the price, in dollars per pound, of Valley Blend tea?

   • $$18$$
   • $$24$$
   • $$18v$$
   • $$5760$$

7. A bakery sells muffins and scones. The price of one muffin is $$m$$ dollars, and the price of one scone is $$s$$ dollars. A customer purchases $$9$$ muffins and $$7$$ scones for a total cost of $$52$$ dollars. The equation $$9m+7s=52$$ models the purchase. Which of the following is the best interpretation of the number $$52$$?

   • The total number of baked goods purchased
   • The total cost, in dollars, of the muffins
   • The total cost, in dollars, of the entire purchase
   • The difference between the price of a muffin and a scone

8. A school fundraiser sells candy bars for $$2.75$$ dollars each and popcorn bags for $$4.25$$ dollars each. In addition, the fundraiser received a fixed donation of $$350$$ dollars. The equation $$2.75c+4.25p+350=1850$$ represents the total amount raised, where $$c$$ is the number of candy bars sold and $$p$$ is the number of popcorn bags sold. Which of the following is the best interpretation of the number $$350$$?

   • The total revenue from popcorn sales
   • The number of items sold
   • The total amount, in dollars, received from a fixed donation
   • The total revenue from candy bar sales

9. What is the solution to the equation $$\frac{x}{4}+\frac{x}{6}=35?$$

   • 84

10. A coffee distributor sells two types of coffee beans: Estate Blend and Classic Blend. The equation $$7E+5C=560$$ represents the total revenue, in dollars, from selling $$E$$ pounds of Estate Blend and $$C$$ pounds of Classic Blend. According to the equation, how many dollars does one pound of Estate Blend cost?

    • $$5$$
    • $$7$$
    • $$80$$
    • $$560$$