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Lesson 9: Use Patterns to Write and Solve Equations — Practice Questions

  1. 1. A table shows the relationship between the number of spiders, $s$, and the total number of legs, $L$. Which equation correctly represents this pattern?

    • A. $L = s + 7$
    • B. $L = 6s$
    • C. $L = 8s$
    • D. $s = 8L$
  2. 2. A table shows the relationship between the number of songs downloaded, $d$, and the total storage used in megabytes, $m$. Based on the pattern $m = 4d + 5$, the storage used for 10 songs is ___ megabytes.

  3. 3. A planter starts with 150 liters of water. Each day, 9 liters are used to water plants. The amount of water remaining, $w$, after $d$ days is given by $w = 150 - 9d$. After 12 days, ___ liters will remain.

  4. 4. The table shows the total cost, $C$, for a pizza with a certain number of toppings, $t$. Which equation describes the relationship between the cost and the number of toppings?

    • A. $C = 1.50t + 12$
    • B. $C = 12t + 1.50$
    • C. $C = t + 13.50$
    • D. $C = 15t$
  5. 5. The table shows the relationship between Leo's age, $L$, and his sister Maria's age, $M$. The pattern is $M = L - 6$. When Leo is 19 years old, Maria will be ___ years old.

  6. 6. A high-speed train travels at a constant speed. The table shows the distance, $d$ (in km), it covers in $t$ hours. How many kilometers will the train travel in 6 hours? | Hours, $t$ | Distance, $d$ (km) | |------------|--------------------| | 2 | 500 | | 3 | 750 | | 5 | 1250 | Answer: ___ km

  7. 7. A phone battery starts at 100% and loses charge at a constant rate. The table shows the remaining percentage of battery, $p$, after $h$ hours of use. Which equation describes this relationship? | Hours, $h$ | Battery %, $p$ | |------------|----------------| | 1 | 85 | | 2 | 70 | | 3 | 55 |

    • A. $p = 100 - 15h$
    • B. $p = 85 - 15h$
    • C. $p = 100 + 15h$
    • D. $p = 15h$
  8. 8. A video game creator is designing levels. The number of gems, $g$, needed to unlock the next world is given by the equation $g = 40L + 10$, where $L$ is the current level. How many gems are needed for a player on level 8? ___ gems

  9. 9. The table shows the relationship between the number of sides of a polygon, $s$, and the number of diagonals, $d$, from a single vertex. Which equation represents the pattern in the table? | Sides, $s$ | Diagonals, $d$ | |------------|----------------| | 4 | 1 | | 5 | 2 | | 6 | 3 |

    • A. $d = s + 3$
    • B. $d = s - 3$
    • C. $d = 3s$
    • D. $d = s \div 4$
  10. 10. A factory produces bottles of juice. The table shows the total number of bottles, $b$, produced by $m$ machines running simultaneously. Following this pattern, how many bottles would 11 machines produce? | Machines, $m$ | Bottles, $b$ | |---------------|--------------| | 3 | 225 | | 5 | 375 | | 8 | 600 | Answer: ___ bottles