Question 1066651: Maria was collecting money for the homeless and she lost the can with the money. she's frantic. She is trying to figure out as best as she can, how much money she had. she doesn't want to cheat anyone but she doesn't have much money to spare. she knows she had nickels, quarters and dimes in the can the last time her friend checked an hour ago. she had five more dimes than quarters and an equal amount of quarters and nickels. Her friend also checked the total amount and saw that there was $2.50. Other people have stopped by and put in the same amount of quarters and nickels that there was when her friend checked earlier. Three people gave dimes. she estimates that at most there was $4 in the can. Is she correct? Can you help Maria and suggest how much she would give to the homeless based on the information she had?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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