SOLUTION: PLEASE HELP ME WITH THIS. THE QUESTION IS "A PERSON HAS 20 COINS IN NICKELS AND DIMES WITH A COMBINED VALUE OF $1.60. DETERMINE THE NUMBER OF COINS AND WHAT TYPE." WHAT FORMULA

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Question 59758: PLEASE HELP ME WITH THIS. THE QUESTION IS "A PERSON HAS 20 COINS IN NICKELS AND DIMES WITH A COMBINED VALUE OF $1.60. DETERMINE THE NUMBER OF COINS AND WHAT TYPE." WHAT FORMULA DO I USE TO SOLVE?
Found 2 solutions by checkley71, funmath:
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
LET N= THE NUMBER OF NUICLES & D = THE NUMBER OF DIMES THEN
YOU NEED TWO FORMULAS AS YOU HAVE TWO UNKNOWNS.
N+D=20 OR N=20-D
SEEING AS A NICKEL IS WORTH 5 CENTS AND THE DIMES ARE WORTH 10 CENTS THEN
5N+10D=160
SUBSTITUTING (20-D)FOR N IN EQUATION #2 WE GET
5(20-D)+10D=160
100-5D+10D=160
5D=60
D=60/5
D=12 NUMBER OF DIMES THEN
N+12=20
N=20-12
N=8 NUMBER OF NICKELS
PROOF
5*8+12*10=160
40+120=160
160=160

Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website!
PLEASE HELP ME WITH THIS. THE QUESTION IS "A PERSON HAS 20 COINS IN NICKELS AND DIMES WITH A COMBINED VALUE OF $1.60. DETERMINE THE NUMBER OF COINS AND WHAT TYPE."
These are easier to solve in terms of cents to avoid decimals.
Let the number of dimes be: x
Then the amount of money we have in dimes is: 10x (in cents)
The rest of the 20 coins are nickels: 20-x
Then the amount of money in nickels is: 5(20-x)
The total amount of money in cents is: 160
10x+5(20-x)=160
10x+100-5x=160
5x+100=160
5x+100-100=160-100
5x=60
5x/5=60/5
x=12
The number of dimes: x=12
The number of nickels: 20-x=20-12=8
:
Check are 12 dimes and 8 nickels = to $1.60?
12($.10)+8($.05)=$1.60
$1.20+$.40=$1.60
$1.60=$1.60 We're right!
Happy Calculating!!!