A stack of nickel and dimes is worth $2.55. How do you find the number of nickels if the number of dimes is less than twice the number of nickels?

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A stack of nickel and dimes is worth $2.55. How do you find the number of nickels if the number of dimes is less than twice the number of nickels?

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Answer 1 · 2016-02-28T00:28:17

The number of nickels could be any odd number between 11 and 51 inclusive.

Explanation:

If $n$ $n$ is the number of nickels and $d$ $d$ is the number of dimes:

$n$ $n$ must be odd Since $$ 2.55$ $$2.55$ can not be made up from an even number $\times 0.05$ $xx0.05$ plus any number $\times 0.10$ $xx0.10$

If $d = 0$ $d=0$ then $n = 51$ $n=51$
If $d = 1$ $d=1$ then $n = 49$ $n=49$
if $d = 2$ $d=2$ then $n = 47$ $n=47$
...and so on

We are told that $d < 2 n$ $d < 2n$ but this only places an lower limit on $n$ $n$ :
$XXX$ $color(white)("XXX")$ Since $5 n + 10 d = 255$ $5n+10d =255$
$XXX \to n + 2 d = 51$ $color(white)("XXX")rarr n+2d=51$
$XXX$ $color(white)("XXX")$ and since $2 n > d$ $2n > d$
$XXX \to n + 4 n > 51$ $color(white)("XXX")rarr n+4n > 51$
$XXX \to 5 n > 51$ $color(white)("XXX")rarr 5n > 51$
$XXX$ $color(white)("XXX")$ and since $n$ $n$ must be an integer
$XXX \to n \geq 11$ $color(white)("XXX")rarr n >= 11$

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A stack of nickel and dimes is worth $2.55. How do you find the number of nickels if the number of dimes is less than twice the number of nickels?

1 Answer

Explanation:

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