Jaxson has xx nickels and yy dimes, having a maximum of 26 coins worth at least $1.80 combined. A maximum of 8 of the coins are nickels and no less than 18 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
Let's solve the given system of inequalities step by step:
1. Let's start by defining the variables:
Let "x" be the number of nickels.
Let "y" be the number of dimes.
2. The number of nickels is given as "A maximum of 8," so we have the inequality: x ≤ 8.
Let's graph this inequality first. The graph will be a vertical line passing through the point (8,0).
3. The number of dimes is given as "No less than 18," so we have the inequality: y ≥ 18.
Let's graph this inequality next. The graph will be a horizontal line passing through the point (0,18).
4. The total number of coins is given as "A maximum of 26 coins," so we have the inequality: x + y ≤ 26.
Let's graph this inequality as well. The graph will be a slanted line with negative slope passing through the points (26,0) and (0,26).
5. The combined value of the coins should be at least $1.80, so we have the inequality: 0.05x + 0.10y ≥ 1.80.
Let's graph this inequality on the same coordinate plane. To do this, let's rewrite the inequality as: y ≥ 18 - 0.5x + 9.
The graph will be a line with negative slope equal to -0.5 passing through the point (0,18) as shown below:
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|/_________
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We need to find the feasible region, which is the area where all four graphs intersect.
By observing the graphs, we can see that the feasible region is a trapezoid-like shape that is bounded by the lines x=0, x=8, y=18, and the line passing through (26,0) and (0,26).
One possible solution within this region is (x, y) = (5, 21), which means Jaxson has 5 nickels and 21 dimes.
Therefore, one possible solution to the given system of inequalities is Jaxson having 5 nickels and 21 dimes.