Linear Equations, Systems & Real-World Models

Practice Questions

Level 1: Easy (Foundational)

1. Solve $4x - 5 = 11$.
   A) $3$
   B) $4$
   C) $5$
   D) $16$
2. Which pair $(x,y)$ satisfies $x + y = 10$ and $x - y = 2$?
   A) $(6, 4)$
   B) $(4, 6)$
   C) $(5, 5)$
   D) $(7, 3)$
3. A car rental is $\$40$ per day plus $\$0.20$ per km. Determine the exact cost, in dollars, of a $3$-day rental with $250$ km. (SPR)

Level 2: Medium (Standard)

1. A company's cost is $C = 20n + 500$ and revenue is $R = 45n$. Determine the exact break-even $n$.
   A) $18$
   B) $20$
   C) $25$
   D) $30$
2. A $30\%$ acid solution is mixed with a $60\%$ acid solution to form $10$ L of $45\%$ acid. How many litres of the $30\%$ solution are needed?
   A) $3$ L
   B) $4$ L
   C) $5$ L
   D) $6$ L
3. A phone plan is $\$20$/mo plus $\$0.10$ per minute. Determine the exact minutes for a bill of $\$45$. (SPR)
4. Line $\ell$ passes through $(0, -3)$ and $(4, 5)$. Which is the equation of $\ell$?
   A) $y = 2x - 3$
   B) $y = 2x + 3$
   C) $y = -2x - 3$
   D) $y = \tfrac{1}{2}x - 3$

Level 3: Hard (Advanced)

1. Two runners start together; one runs at $6$ km/h and the other at $8$ km/h in the same direction. After how many hours is the faster one $5$ km ahead?
   A) $2.0$
   B) $2.5$
   C) $3.0$
   D) $5.0$
2. A budget line is $2x + 3y = 60$. Determine the maximum integer value of $y$ when $x \ge 3$. (SPR)
3. Three consecutive integers sum to $126$. Determine the largest integer.
   A) $41$
   B) $42$
   C) $43$
   D) $44$