Free Year 9 Expand a linear expression Practice | Skillo

Question 1 — Easy

Priya is training for a school swimming carnival. She swims a total of 15 laps, which is 3 more than twice the number of laps she swam yesterday. Which equation represents this situation, and what is the solution?

Answer: The equation is 2x + 3 = 15. Subtracting 3 from both sides gives 2x = 12, then dividing by 2 gives x = 6. Substituting back: 2(6) + 3 = 15 ✓. Option A results from dividing 15 by 3 instead of solving the equation. Option C adds 3 instead of subtracting it. Option D halves 15 without accounting for the +3.

Question 2 — Medium

Zac and Mei are collecting cans for a school fundraiser. Together they have collected 45 cans. Zac collected 3 more than twice the number Mei collected. How many cans did Mei collect?

Answer: Let m = the number of cans Mei collected. Then Zac collected 2m + 3. The equation is m + (2m + 3) = 45, which simplifies to 3m + 3 = 45, giving 3m = 42, so m = 14. Substituting back: Mei = 14, Zac = 31, total = 45 ✓. Option B (16) gives Zac = 35, total = 51 ≠ 45. Option C (21) gives Zac = 45, total = 66 ≠ 45. Option D (24) gives Zac = 51, total = 75 ≠ 45.

Question 3 — Hard

Priya is saving money to buy a new volleyball. She already has $14.50 and earns $8.50 per hour helping at a community garden. The volleyball costs $40. Which equation correctly models how many hours, h, Priya needs to work, and what is the solution?

Answer: Option A is correct — The equation is 8.50h + 14.50 = 40. Subtracting 14.50 from both sides gives 8.50h = 25.50, and dividing by 8.50 gives h = 3. Option B gives 2.5 hours, which when substituted gives 8.50(2.5) + 14.50 = 35.75 ≠ 40. Option C uses the wrong equation.