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Nichelle has x dimes and y nickels. She has at least 11 coins worth a maximum of $0.80 combined. Solve the system of inequalities graphically and determine one possible solution.

Nichelle has x dimes and y nickels. She has at least 11 coins worth a maximum of $0.80 combined-example-1
User Nur Rony
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1 Answer

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A graph of the system of inequalities is shown in the image and one possible solution is the ordered pair (2, 10).

Nichelle can have 2 dimes and 10 nickels.

In order to solve these system of inequalities graphically, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

  • Let x represent number of dimes.
  • Let y represent number of nickels.

Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.

Since Nichelle has at least 11 coins worth a maximum (at most) of $0.80 combined, a linear inequality to represent this is given by;

x + y ≥ 11

y ≥ 11 - x

For a maximum of $0.80 combined, we have:

0.1x + 0.05y ≤ 0.80

y ≤ -2x + 16

Based on the graph (see attachment), a possible solution is given by the ordered pair (2, 10). Therefore, Nichelle can have 2 dimes and 10 nickels worth of coins.

Nichelle has x dimes and y nickels. She has at least 11 coins worth a maximum of $0.80 combined-example-1
User Jonathan Rich
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