Problema Solution
Joe has a collection of nickels and dimes that is worth $4.35. If the number of dimes were doubled and the number of nickels were increased by 10, the value of the coins would be $7.05. How many dimes does he have?
Answer provided by our tutors
Let x be the number of nickels and y the number of dimes then
.05x + .10y = 4.35 Twice as many dimes would be 2y and 10 more nickels would be x + 10 so the second equation would be
(x + 10).05 + 2y(.10) = 7.05 or .05x + .5 + .2y = 7.05 or .05x + .2y =6.55 Putting them together we have
.05x + .2y = 6.55 and
.05x + .1y = 4.35 subtracting the second from the first we get
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.1y = 2.20 so y = 22 or 22 dimes and 43 nickels
Double the dimes is 44 or 4.40 and 10 more nickels is 53 is 2.65 which does indeed total to $7.05