Melissa has $2.35 in nickels and dimes. If she has 33 coins in all, how do you find the number of nickels and dimes?

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Answer 1 · 2018-07-03T22:22:21

#N = 19, D = 14#

Given: #$2.35# in nickels and dimes, #33# coins in all

There are always 2 equations in these types of problems.

The first equation is the quantity equation and the second is the value equation.

The value of a nickel is 5 cents, the value of a dime is 10 cents and #$2.35 = 235# cents.

Let #N = "number of nickels and "D = "number of dimes"#

quantity equation: #" "N + D = 33#

value equation: #" "235 = 5N + 10D# or #2.35 = .05N + .1D#

I think it's easier to not have decimals, so I will be using the first value equation.

We can rewrite the quantity equation to use substitution: #N = 33 - D#

Substitute this into the value equation:

#5(33-D) + 10D = 235#

#165 - 5D + 10D = 235#

#165 + 5D = 235#

#5D = 235 - 165 = 70#

#D = 70/5 = 14#

#N = 33-14 = 19#