Solve one, any question you want, please show work,

Step 1: Variables are q for quarters and d for dimes. So d = dimes and q = quarters

Step 2: The two equations that form a system of equations are:

Step 3: Work is shown on the attachment and on the step-by-step explanation

Step 4: Given the context of the problem, the solution of the amount of dimes and quarters, which is 7 dimes and 12 quarters, is needed to satisfy both systems to concur that there was 7 dimes and 12 quarters in a sum of money that amounted to $3.70 with 19 coins in total.

Step-by-step explanation:

Step 1: To first attempt to solve this, we must have to set up two variables for the amount of value a quarter and a dime has. So since a quarter is worth 0.25¢ in and a dime is worth 0.10¢, then we can set up one of the equations to be:

And we set it to equal the $3.70 because that's the amount that the sum of money totals to.

Step 2: Now to get the other side of the equation, we use the variables again, d and q and set that to equal 19 because that is the amount of coins that there is in total.

Step 3: Now that we have both equations, we can solve the problem now.

Let's first solve this equation by setting one of the side's variables the same absolute value, but not the same integer value so that we can cross it off. I will choose the equation to be multiplied by -.1 so that we can cross off both 0.1d and -0.1d after the result of the multiplication:

Now, lets cross off everything that we can, and add up the variables together. This includes adding .25q + (-.1q) and adding 3.70 + -1.9.

Now we have:

Now, what we do from here is add the left side and the right side side to get one equation, which is:

Finally, we divide both sides to get q=12, which means that there are 12 quarters. Since there are 19 coins in total, we can subtract 12 from 9 to get the remaining amount of dimes, which is 7.

In conclusion, q=12 and d=7.

My written work is also provided in the attachment!!!

Step 4: What does this mean in the context of the question?

This basically means that the solution of the amount of dimes and quarters, which is 7 dimes and 12 quarters, is needed to satisfy both systems to concur that there was 7 dimes and 12 quarters in a sum of money that amounted to $3.70 with 19 coins in total.

In simpler terms, this means that we need 7 dimes and 12 quarters to satisfy that there was a sum of money that amounted to $3.70 with 19 coins in total .

details

step-by-step explanation: