.
You can solve it in this way, using one single equation
D + (D + 9) = 21 coins
2D = 21 - 9 = 12
D = 12/2 = 6
obtaining the answer 6 one-dollar coins and 6+9 = 15 quarters.
Or, alternatively, you can write a system of two equations
Q + D = 21
Q - D = 9
and then add the equations, obtaining
2Q = 21 + 9 = 30
Q = 30/2 = 15 quarters and 15-9 = 6 one-dollar coins.
You can choose any of these two way - they lead you to the same answer.
Solved, explained and completed.
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To see a million other similar solved problems, look into the lesson
- Word problems that lead to a simple system of two equations in two unknowns
in this site.