Luis is saving money to purchase a new video game. He has a total of 30 coins consisting of nickels and dimes. The value of the coins is $2.20. Let n represent the number of nickels and let d represent the number of dimes. Which system of equations can be used to determine the number of nickels and the number of dimes Luis has?

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Verified Answer :

l0velyy l0velyy · Answer 1 · 2016-11-08T18:05:52-05:00

n + d = 30 and 5n + 10d =220

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chisnau chisnau · Answer 2 · 2019-06-29T03:43:43-04:00

Answer:

$n+d=30$ and

$0.05n+0.10d=2.20$

Step-by-step explanation:

Let n represent the number of nickels

Let d represent the number of dimes.

Luis has a total of 30 coins; equation becomes:

$n+d=30$

or $n=30-d$ ..... (1)

The value of the coins is $2.20 ; equation becomes:

{a dime is worth 10 cents and a nickel is 5 cents}

$0.05n+0.10d=2.20$ ..... (2)

Putting the value of n from (1) in (2)

$0.05(30-d)+0.10d=2.20$

=> $1.5-0.05d+0.10d=2.20$

=> $0.05d=2.20-1.5$

=> $0.05d=0.7$

=> d=14

And n=30-d

so, $n=30-14=16$

So, the system of equations used to determine the number of nickels and the number of dimes Luis has are :

$n+d=30$ and

$0.05n+0.10d=2.20$