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Lesson 59: Solving Systems of Linear Equations by Substitution — Practice Questions

  1. 1. A farm has 30 animals, consisting of chickens (2 legs) and pigs (4 legs). There are 80 legs in total. Let $c$ be chickens and $p$ be pigs. Which system of equations models this situation?

    • A. $c + p = 30$ and $2c + 4p = 80$
    • B. $c + p = 80$ and $2c + 4p = 30$
    • C. $c + p = 30$ and $4c + 2p = 80$
    • D. $2c + 4p = 30$ and $c + p = 80$
  2. 2. A bakery sold 40 items, including cookies for 2 dollars each and brownies for 3 dollars each. If the total sales were 105 dollars, how many brownies were sold? ___

  3. 3. Simplify the expression $(2a^5b^{-3})^4$. Write your answer using only positive exponents. ___

  4. 4. Which expression is equivalent to $(5m^2n^3)^2$?

    • A. $25m^4n^6$
    • B. $5m^4n^6$
    • C. $10m^4n^6$
    • D. $25m^4n^5$
  5. 5. A player answers 20 questions in a trivia game. Easy questions are worth 3 points and hard questions are worth 5 points. If the player scored 76 points, how many hard questions did they answer? ___

  6. 6. A farm has 30 animals, consisting of chickens ($c$) and pigs ($p$). There are 80 legs in total. Chickens have 2 legs and pigs have 4. Which system of equations models this situation?

    • A. $\{c + p = 80, 2c + 4p = 30\}$
    • B. $\{c + p = 30, 2c + 4p = 80\}$
    • C. $\{c + p = 30, 6(c+p) = 80\}$
    • D. $\{2c = 30, 4p = 80\}$
  7. 7. A school sold 50 items at a fundraiser, earning 85 dollars. Candy bars ($c$) cost 2 dollars and sodas ($s$) cost 1 dollar. How many candy bars were sold? ___

  8. 8. A theater sold 100 tickets for 2600 dollars. General tickets ($g$) cost 20 dollars and VIP tickets ($v$) cost 50 dollars. After substituting to solve for $v$, which equation results?

    • A. $g + (100-g) = 100$
    • B. $20g + 50(100-g) = 2600$
    • C. $20(100-v) + 50v = 2600$
    • D. $g + v = 100$
  9. 9. A parking lot contains 25 vehicles, which are either cars ($c$) or motorcycles ($m$). There is a total of 80 wheels. If cars have 4 wheels and motorcycles have 2, how many motorcycles are in the lot? ___

  10. 10. A stand sells apples ($a$) for 2 dollars and oranges ($o$) for 3 dollars. In one day, 50 fruits were sold for 120 dollars. Which statement correctly describes the equations for this problem?

    • A. $a+o=120$ is the quantity equation and $2a+3o=50$ is the value equation.
    • B. $a+o=50$ represents the total cost of the fruits.
    • C. $2a+3o=120$ represents the total number of fruits sold.
    • D. $a+o=50$ represents the total number of fruits, and $2a+3o=120$ represents the total cost.