Diana has a total of $2.40 in quarters and dimes in her purse. If she has a total of 15 coins, how many dimes and how many quarters does she have?

Answer 1

Let x = number of dimes. Then, 15 - x = number of quarters.

Value of dimes + value of quarters = 2.40

0.10x + 0.25(15 - x) = 2.40

0.10x + 3.75 - 0.25x = 2.40

-0.15x = -1.35

x = 9

So, there are 9 dimes and 6 quarters.

Answer 2

Let x = number of quarters and y = number of dimes.

First equation: x + y = 15 (to represent the number of coins Diana has)

Second equation: 0.25x + 0.10y = 2.40 (to represent the total in dollars that Diana has)

From here we can use these two equations to solve for the variables.

Starting with the first equation:

x + y = 15

x = 15 - y

Then substitute into the second equation:

0.25(15 - y) + 0.10y = 2.40

Distribute and simplify to solve for y.

3.75 - 0.25y + 0.10y = 2.40

3.75 - 0.15y = 2.40

-0.15y = -1.35

y = 9

We know that Diana has 9 dimes. Plug this value back into the first equation to find the number of quarters.

x + y = 15

x + 9 = 15

x = 6

Diana has 6 quarters.

We can check this by inputing x = 6 and y = 9 into the second equation.

0.25(6) + 0.10(9) = 2.40

2.40 = 2.40

Hope this helps!