Question 1138522: Ben was describing his coin collection to his friends. He said I have 1.45 pesos more in 5 centavos (nickels) than in 10 centavos (dimes). Ii I had two 5 centavos (nickels) less, I would have 5 times as many 5 centavo (nickels) as 10 centavos (dimes). How many coins of each kind does he have?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the number of persos needs to be 145 and not 1.45.
there are 100 pesos to the dollar.
therefore 1.45 dollars worth of pesos is equal to 145 pesos.
you could work this problem in dollars, but it's easier to work it in pesos.
i'll do both to sh ow you the difference.
you are given that the number of nickels is equal to the number of dimes plus 145 pesos.
the value of a nickel is 5 peros.
the value of a dime is 10 pesos.
if you let x equal the number of nickels and y equal the number of dimes, then your first equation is:
5x = 10y + 145.
this equations tells you that the number of nickels times 5 pesos per nickel is equal to the the number of dimes times 10 pesos per dime plus 145 pesos.
you are told that if you had 2 less nickels, then the number of nickels would be equal to 5 times the number of dimes.
the equation for this is x - 2 = 5y.
solve for x in this equation to get x = 5y + 2.
in the first equation of 5x = 10y + 145, replace x with 5y + 2 to get:
5 * (5y + 2) = 10y + 145
simplify to get 25y + 10 = 10y + 145
subtract 10y from both sides of the equation and subtract 10 from both sides of the equation to get:
25y - 10y = 145 - 10
simplify to get 15y = 135
solve for y to get y = 9.
since x is equal to 5y + 2, you get x = 47.
you have x = 47 and y = 9.
your original equation is 5x = 10y + 145.
replace x with 47 and y with 9 to get 5 * 47 = 10 * 9 = 145.
simplify to get 235 = 90 + 145 which becomes 235 = 235 which confirms the solution is correct.
now back to the beginning.
you were given 1.45 in pesos (not 1.45 pesos).
since you are working in dollars, then anickel is equal to .05 dollars and a dime is equal to .10 dollars.
your first equaiton becomes .05 * x = .10 * y + 1.45
you are then given that x - 2 = 5 * y which results in x = 5y + 2.
you then replace x with 5y + 2 to get .05 * (5y + 2) = .10 * y + 1.45
simplify to get .25 * y + .10 = .10 * y + 1.45
subtract .10 * y from both sides of the equation and subtract .10 from both sides of the equation to get:
.25 * y - .10 * y = 1.45 - .10
simplify to get .15 * y = 1.35
solve for y to get y = 9
since x = 5y + 2, you get x = 47.
replacing y with 9 and x with 47 in the original equation of .05 * x = .10 * y + 1.45 gets you.
.05 * 47 = .10 * 9 + 1.45 which results in 2.35 = .9 + 1.45 which results in 2.35 = 2.35 which confirms the solution is good.
the difference is that, the first time i worked in pesos and the second time i worked in dollars.
145 pesos equals 1.45 in dollars.
5 pesos per nickel equals .05 dollars per nickel.
10 pesos per dime equals .10 dollars per dime.
Answer by greenestamps(13200)  (Show Source):
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