Algebraic Thinking Flashcards

Sarah earns $9 per hour. Which inequality shows how many hours (h) she must work to earn at least $63?

Answer: 9h ≥ 63

'At least $63' means her earnings must be $63 or more, so the inequality is 9h ≥ 63.

Two friends split a restaurant bill equally, and each pays $14. Which equation finds the total bill (b)?

Answer: b ÷ 2 = 14

If the bill is divided equally between 2 people and each pays $14, then b ÷ 2 = 14, giving a total of $28.

The perimeter of a square is given by P = 4s, where s is the side length. If the perimeter is 36 inches, what is the side length?

Answer: 9 inches

Set up the equation 4s = 36 and divide both sides by 4 to get s = 9 inches.

A store sells notebooks for $3 each. Which expression shows the money remaining after buying n notebooks if you start with $20?

Answer: 20 - 3n

You start with $20 and spend $3 per notebook, so money remaining = 20 - 3n.

Which equation has a solution of x = -3?

Answer: x + 5 = 2

Substituting x = -3 into x + 5 = 2 gives -3 + 5 = 2, which is a true statement.

A recipe calls for 2 cups of flour per batch of cookies. Which expression gives the total cups needed for b batches?

Answer: 2b

If each batch needs 2 cups, then b batches require 2 × b = 2b cups of flour in total.

A sequence follows the rule 'multiply by 3': 2, 6, 18, 54, ___. What is the next term?

Answer: 162

Each term is multiplied by 3 to produce the next term: 54 × 3 = 162.