A bag of dimes and quarters is worth $6.20. There is one less thantwice as many dimes as quarters. How many of the coins are dimes?

Answer 1

Let's break this down into two equations, where we will solve for two unknown variables.

x = number of quarters

y = number of dimes

.25x + .10y = 6.20

y = 2x - 1

The first equation is handling the values of this money, and the second is handling the logic (we have one less than twice as many dimes as we do quarters).

Now we solve the system of equations, and look! A perfect system for substituting y into the first equation.

.25x + .10(2x -1) = 6.20

Excellent, now we just solve for x, keeping in mind our order of operations, then we figure out y from there by putting it into our second equation with our known x value.

For reference, I got 14 quarters and 27 dimes. I can always go back and double check by plugging those into my two original equations, and they check out!

*Note that the question is only asking to report the number of dimes*

Answer 2

D is the # of dimes

Q is the # of quarters

There is one less than twice as many dimes as quarters...

The # of dimes is one less than twice as many as # of quarters...

D = 2Q-1

The total amount is $6.20 which is 620 pennies

10(2Q-1) + 25Q = 620

20Q - 10 + 25Q = 620

45Q - 10 = 620

45Q = 630

Q = 630/45 = 210/15 = 70/5 = 14

14 quarters ---> 2(14)-1 = 28-1 = 27 dimes

27 dimes + 14 quarters =

$2.70 + $3.50 = $6.20