descriptionabcddiagramequationinput = 5[br]output = ?independent[br]variabledependent[br]variable

If we apply the steps to a generic 3-digit number x, the result is13(11(7x+1)−5)−78=1,001xFor any 3-digit number x, the number 1,001x is just that number repeated twice.  This works since 1,001x=1,000x+x, so for example, 1,001⋅314=1,000⋅314+1⋅314=314,000+314=314,314

[list=1][*]115. If q=4, then the equation tells us that 0.1d+(0.25)⋅4=12.5. Subtracting 1 from both sides gives 0.1d=11.5, so d=115.[/*][*]100. If q=10, then the equation tells us that 0.1d+(0.25)⋅10=12.5. Subtracting 2.5 from both sides gives 0.1d=10, so d=100.[/*][*]Yes. If you know the number of quarters, then you can determine the number of dimes from the equation. We can even write the equation in a way that shows this: d=125−2.5q. The expression 125−2.5qrepresents the output—it is the rule that determines the output d from a given input q.[/*][*]40. If d=25, then the equation tells us that 0.1(25)+(0.25)q=12.5. Subtracting 2.5 from both sides gives .25q=10, so q=40.[/*][*]38. If d=30, then the equation tells us that 0.1(30)+(0.25)q=12.5. Subtracting 3 from both sides gives .25q=9.5, so q=38.[/*][*]Yes. If you know the number of dimes, then you can determine the number of quarters from the equation. We can even write the equation in a way that shows this: q=50−0.4d. The expression 50−0.4drepresents the output—it is the rule that determines the output q from a given input d.[/*][/list]