Question 1066651
a dime is worth .10 dollars.
a nickel is worth .05 dollars.
a quarter is worth .25 dollars.


your starting formula is:


.10 * d + .25 * q + .05 * n = 2.5


d = number of dimes.
q = number of quarters.
n = number of nickels.


you are told that the number of dimes is 5 more than the number of quarters.


start with d = q + 5.
solve for q to get q = d - 5.


you are told that the number of nickels and quarters is the same.


this means that d must be equal to n + 5 as well.
solve for n to get n = d - 5.


your formula of .10 * d + .25 * q + .05 * n = 2.5 becomes .10 * d + .25 * (d-5) + .05 * (d-5) = 2.5


simplify this formula to get .10 * d + .25 * d - .25 * 5 + .05 * d - .05 * 5 = 2.5


simplify further to get .10 * d + .25 * d - 1.25 + .05 * d - .25 = 2.5


combine like terms to get .40 * d - 1.5 = 2.5


add 1.5 to both sides of this equation to get .40 * d = 4.00


solve for d to get d = 10


since d = q + 5, and since d = n + 5, then q = 5 and n = 5.


your equation of .10 * d + .25 * q + .05 * n = 2.5 becomes .10 * 10 + .25 * 5 + .05 * 5 = 2.5


simplify to get 1 + 1.25 + .25 = 2.5


combine like terms to get 2.5 = 2.5


the solution looks good.


d = 10 and q = 5 and n = 5 is the amount of money she had just prior to when she lost it.


since then, the same amount of quarters and nickels was put in the box plus 3 people gave one dime apiece.


this means that 5 more quarters and 5 more nickels and 3 more dimes were added.


5 quarters * .25 = 1.25
5 nickels * .05 = .25
3 dimes = .30


the total added money was 1.80.


2.50 + 1.80 = 4.30


her estimate is off by 30 cents.


she should give 4.30 to the homeless based on these calculations.