Question 1141884
6.90 = 690 cents.
q is the number of quarters
d is the number of dimes


you get two equations.


first equation is 25 * q + 10 * d = 690


this is because each quarter is worth 25 cents and each dime is worth 10 cents.


second equation is 10 * q + 25 * d = 780


this is because each quarter is worth 10 cents and each dime is worth 25 cents.


the number of quarters and dimes is the same.


what is changed is their value as stated in the problem statement.


your two equations that need to be solved simultaneously are:


25 * q + 10 * d = 690
10 * q + 25 * d = 780


multiply both sides of the second equation by 2.5 and leave the first equation as is to get:


25 * q + 10 * d = 690
25 * q + 62.5 * d = 1950


subtract the first equation from the second to get:


52.5 * d = 1260


solve for d to get d = 24


the first equation of 25 * q + 10 * d = 690 becomes 25 * q + 10 * 24 = 690


simplify to get 25 * q + 240 = 690


subtract 240 from both sides to get 25 * q = 450


solve for q to get q = 18


you have 18 quarters and 24 dimes.


if the value of the quarters is 25 cents and the value of the dimes is 10 cents, the total value is 25 * 18 + 10 * 24 = 690.


if the value of the quarters is 10 cents and the value of the dimes is 25 cents, the total value is 10 * 18 + 25 * 24 = 780.


the solution is confirmed to be good.


the solution is that the number of quarters is 18.