Systems of equations word problems

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Learn it Name the two unknowns, write one equation for each fact (a count and a total value, a sum and a difference…), then solve by substitution or elimination.

Example: 30 coins, dimes and quarters, worth $\$4.50$. How many quarters?

$d + q = 30$ and $10d + 25q = 450$.
Multiply the first by 10: $10d + 10q = 300$.
Subtract: $15q = 150$, so $q = 10$ quarters.

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