Question

Diego is collecting dimes and nickels in a jar. He has collected $22.25 so far. The relationship between the numbers of dimes and nickels, and the amount of money in dollars is represented by the equation .

Select all the values (d,n) that could be solutions to the equation.

Answer 1

One solution is x = 1 and y = 443 because
0.10(1) + 0.05(443) = 22.25.
So, (1, 443) is a solution.
Since, 1 dime = 2 nickels,
Increment of 1 in x-value = Decrease of 2 in y-value.
Therefore, the set of possible solutions are {(1, 443), (2, 441), (3, 439), (4, 437),......(222, 1)}

Hope this helped, if not let me know my error. :)