The key idea
Name the two unknowns, then write one equation for each fact: usually a count and a total value. Read relationships like “3 fewer than twice” carefully, then solve by substitution or elimination. Check that the answer is the quantity the question asks for.
The trap
Answering with the wrong unknown, or writing “twice as many A as B” as 2a=b.
Can Desmos do it?
Once the equations are written, graphing them finds the intersection instantly. Writing them correctly is the whole problem, and no calculator does that part.
College Board skill: Systems of two linear equations in two variables · Algebra
One question from each level. The drill has 12 at every level, and moves you up after four right in a row.
Level 1 · Warm-up
A school sold 75 tickets to a play. Adult tickets cost $12 and student tickets cost $8, and ticket sales totaled $696. How many adult tickets were sold?
Show the answer
Answer: 24Let a be the adult tickets and s the student tickets: a+s=75 and 12a+8s=696. Replace s with 75−a: 12a+8(75−a)=696, so 4a=96 and a=24.
Level 2 · Test level
A store sold T-shirts for $12 each and hoodies for $30 each. It sold 4 fewer T-shirts than twice the number of hoodies, and sales totaled $762. How many items did the store sell in all?
Show the answer
Answer: 41Let h be the hoodies; then the T-shirts number 2h−4. Sales: 12(2h−4)+30h=762, so 54h=810 and h=15. T-shirts: 2(15)−4=26. In all: 15+26=41. (The question asks for all items, not just hoodies.)
Level 3 · Beyond the test
Notebooks cost $3 each and binders cost $5 each. Buying x notebooks and y binders costs $123. Buying y notebooks and x binders instead would cost $125. What is the value of x+y?
Show the answer
Answer: 31The two facts are 3x+5y=123 and 3y+5x=125. Add them: 8x+8y=248, so 8(x+y)=248 and x+y=31. You never need x and y separately.
Practice all 36 questions
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