Christina has 50 coins consisting of quarters and dimes. The coins combined value is $9.50. Write a system of equation to determine how many quarters and dimes Christina has.

Christina has 30 quarters and 20 dimes.

Step-by-step explanation:

Given that a quarter is worth 0.25 dollars and a dime is worth 0.10 dollars, if Christina has 50 coins and these add up to a total of $ 9.50, to determine the number of quarters and dimes that she has in her possession, the following calculation must be carried out, taking into account that the difference between a quarter and a dime is 0.15 dollars:

50 x 0.25 = 12.5

12.5 - 9.5 = 3

Thus, the difference between the value that Christina has and the value that she would have if all of her coins were quarters is 3 dollars. Thus, since 0.15 x 20 equals 3, of the 50 coins Christina has, 30 are quarters and 20 are dimes.

This is confirmed through the following equation:

30 x 0.25 + 20 x 0.1 = X

7.5 + 2 = X

9.5 = X