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Math Practice

Systems of Equations Word Problems Practice

Name two unknowns, turn two facts into two equations, then solve. Each problem asks for one of the two quantities, so you can check your setup quickly.

  1. 1.

    Two numbers add up to 45 and their difference is 13. What is the larger number?

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    and . Adding gives , so (and ).

  2. 2.

    Adult movie tickets cost $12 and child tickets $7. A group bought 9 tickets for $83. How many adult tickets?

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    , . Substituting : , so .

  3. 3.

    A bake sale sold 120 items: cookies at $1.50 and brownies at $2. It took in $205. How many brownies were sold?

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    , . Substituting : , so .

  4. 4.

    A drawer holds 30 bills, all $5 and $10, worth $220. How many $10 bills are there?

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    , . Subtract 5 times the first: , so .

  5. 5.

    $10,000 is invested, part at 4% and the rest at 6%, earning $520 in a year. How much is invested at 4%?

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    , . Substituting gives , so .

  6. 6.

    $8,000 is split between 3% and 5% accounts, earning $300 a year. How much is in the 3% account?

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    gives , so .

  7. 7.

    How many liters of a 20% acid solution must be mixed with a 50% solution to make 30 L of 40% solution?

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    , . Substituting gives , so L.

  8. 8.

    Candy at $4/lb is mixed with candy at $7/lb to make 12 lb worth $5/lb. How many pounds of the $4 candy are used?

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    , . Substituting gives , so lb.

  9. 9.

    A plane flies 1,200 miles with the wind in 4 hours and back against it in 5 hours. What is the wind speed in mph?

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    and . Subtracting gives , so mph (and ).

  10. 10.

    A boat goes 36 km downstream in 2 hours and back upstream in 3 hours. What is its speed in still water, in km/h?

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    and . Adding gives , so km/h.

  11. 11.

    Fixed costs are $500, each item costs $3 to make and sells for $8. How many items must be sold to break even?

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    Cost , revenue . Setting them equal: , so .

  12. 12.

    A rectangle’s length is 3 cm more than twice its width, and its perimeter is 42 cm. What is the length?

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    and . Substituting: , so and cm.
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MPhil in Mathematics, Founder of Mathovia
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Systems of Equations Word Problems Practice

These problems follow the systems of equations word problems lesson. Use them as a systems of equations word problems worksheet: write “let x = …” before every setup.

Common setups

TypeEquation 1Equation 2
items or tickets
investments
mixtures
wind or current

Common mistakes to watch for

  • Undefined variables. Write what each variable means, with units, before writing equations.
  • Mixing totals and rates. One equation usually counts items; the other counts their value or cost.
  • Unit mismatches. Convert percentages to decimals and minutes to hours before combining.
  • Not checking reasonableness. A negative number of tickets means an equation is set up wrong.

Frequently Asked Questions

How do I set up the two equations?+

One equation usually counts things (items, coins, liters, dollars invested). The other weights each count by its price, value, concentration or rate.

How do wind and current problems work?+

With the wind or current the speeds add; against it they subtract. Write distance = speed × time for each direction.

How do I type money answers?+

Type the number without commas or a dollar sign, for example 4000.

More practice problems

Substitution Method Practice Problems Elimination Method Practice Problems Systems With Three Variables Practice Problems