Grade 10 Academic (MPM2D) · Analytic Geometry

Linear systems word problems

Set up and solve a system of two linear equations from a real-world word problem involving two ticket or item prices. Unlimited questions, five difficulty levels, and a full worked solution every time, included free with weekly lessons.

Practice this skill Curriculum: MPM2D-AG1.2

Try one

At the team fundraiser, the student council sold car wash tickets and bake sale tickets. Car wash tickets cost $15.00 each and bake sale tickets cost $12.00 each. In total, 18 were sold for a combined $252.00. How many car wash tickets were sold?

Answer: 12

See one solved, step by step

At the team fundraiser, the student council sold car wash tickets and bake sale tickets. Car wash tickets cost $20.00 each and bake sale tickets cost $16.00 each. In total, 18 were sold for a combined $324.00. How many car wash tickets were sold?

📘 Worked solution

1a + s = 18 $20.00a + $16.00s = $324.00Let a = number of car wash tickets and s = number of bake sale tickets, then write one equation for the total count and one for the total money.

2a = 18 - sIsolate a in the simpler (counting) equation so it can be substituted into the other.

3$20.00(18 - s) + $16.00s = $324.00Substitute for a in the money equation, leaving only s.

4s = 9, so a = 18 - 9 = 9Distribute and combine like terms to solve for s, then use a = 18 - s to find a.

5There were 9 car wash tickets.That's the number the question asked for.

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