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Worksheet: Solving Equations Mentally

Q1:

The distance 𝑑 Scarlett travels in her car while driving 58 miles per hour for 1.5 hours is given by the equation 𝑑 1 . 5 = 5 8 . How far did she travel?

Q2:

A shop has π‘₯ pounds of vegetables for sale, and two-thirds of them are artichokes. If there are 10 pounds of artichokes, then the equation 2 3 π‘₯ = 1 0 describes this situation. Use this to calculate how many pounds of vegetables there are.

Q3:

A shop has π‘₯ pounds of vegetables for sale, and one-half of them are artichokes. If there are 14 pounds of artichokes, then the equation 1 2 π‘₯ = 1 4 describes this situation. Use this to calculate how many pounds of vegetables there are.

Q4:

Both Jacob and Elizabeth love to ride their motorbikes on the mountain roads. If Jacob rode 24 more miles than Elizabeth did, and he rode 38 miles in total, write an equation that describes the number of miles 𝑣 that Elizabeth rode.

  • A 2 4 𝑣 = 3 8
  • B 𝑣 βˆ’ 2 4 = 3 8
  • C 𝑣 + 3 8 = 2 4
  • D 𝑣 + 2 4 = 3 8
  • E 3 8 𝑣 = 2 4

Q5:

Solve 𝑑 + 4 = 1 . 3 2 for 𝑑 .

Q6:

On average, a goat lives to be 17 years old. Given that this is 4 years less than the average lifespan of a tiger, solve the equation β„Ž βˆ’ 4 = 1 7 to determine the average lifespan of a tiger.

Q7:

The difference between an ostrich’s speed and a chicken’s speed is 31 miles per hour. If an ostrich can run at a speed of 40 miles per hour, solve the equation 4 0 βˆ’ 𝑐 = 3 1 to find the speed a chicken can run 𝑐 .

Q8:

Jacob’s destination is 90 miles away. He drove 80 miles already. Solve 9 0 βˆ’ π‘š = 8 0 , where π‘š represents the number of miles which he has yet to drive, to determine π‘š .

Q9:

State whether the following statement is true or false: In π‘š + 1 3 = 2 1 , the variable π‘š can have any value and be a solution.

  • Afalse
  • Btrue

Q10:

Charlotte went shopping and spent $86.97. She spent 𝑏 dollars on books and $48.52 on CDs. Using the equation 8 6 . 9 7 = 𝑏 + 4 8 . 5 2 , determine the amount that she spent on books.

Q11:

Solve the following equation mentally: 𝑓 Γ· 2 = 5 .