SOLUTION: If Jasmine has 4 more dimes than nickels and they have a combined value of 145 cents, how many of each coin does she have?

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Question 1200041: If Jasmine has 4 more dimes than nickels and they have a combined value of 145 cents, how many of each coin does she have?

Found 3 solutions by josgarithmetic, math_tutor2020, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answers:
7 nickels and 11 dimes


Work Shown:
n = number of nickels
n+4 = number of dimes

5n = value of the nickels (cents)
10(n+4) = 10n+40 = value of the dimes (cents)
5n+(10n+40) = 15n+40 = total value (cents)

total value = 145 cents
15n+40 = 145
15n = 145-40
15n = 105
n = 105/15
n = 7 nickels
n+4 = 7+4 = 11 dimes

Check:
7 nickels = 7*5 = 35 cents
11 dimes = 11*10 = 110 cents
7 nickels + 11 dimes = 35 cents + 110 cents = 145 cents
The answers are confirmed.

Side note: 145 cents = 145/100 = $1.45

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Probably a formal algebraic solution was wanted; the other tutors showed a couple.

But you can get some good mental exercise, and good problem-solving practice, by solving the problem using logical reasoning and simple mental arithmetic -- something like this:

(1) take away the "extra" 4 dimes, leaving equal numbers of nickels and dimes, with a total value of 145-40 = 105 cents
(2) one nickel and one dime together have a value of 15 cents; the number of nickels and dimes required to make 105 cents is 105/15 = 7
(3) that makes 7 nickels and 7 dimes; now add back in the other 4 dimes to give the final answer of 7 nickels and 11 dimes