Question 1077477
d = number of dimes
q = number of quarters


10d = value of dimes in terms of cents.
25q = value of quarters in terms of cents.


tom has 3 times as many quarters as dimes.


therefore q = 3d


25q + 10d = 340


since q = 3d, then replace q with its equivalent value of 3d and the equation becomes:


25 * (3d) + 10d = 340


simplify to get:


75d + 10d = 340


combine like terms to get:


85d = 340


solve for d to get d = 340 / 85 = 4


since q = 3d, then q = 12


tom has 12 quarters and 4 dimes for a total of 12 * 25 + 4 * 10 = 340 cents.


what you are doing is using the concept of equivalent values to reduce the number of unknown variables so you can solve the equation.


since q equals the number of quarters and d equal the number of dimes, and since the number of quarters is equal to three times the number of dimes, you set up the equivalent value of q = 3d.


you then replace q with the equivalent value of 3d in the equation to solve for d.