SOLUTION: This word problem has to do with coins, but I need to solve it by setting up and solving a system of two linear equations in two variables. Cindy has 43 coins consisting of nick

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Question 60293This question is from textbook Elementary and Intermediate Algebra
: This word problem has to do with coins, but I need to solve it by setting up and solving a system of two linear equations in two variables.
Cindy has 43 coins consisting of nickels and dimes. The total value of the coins is $3.40. How many coins of each kind does she have?
I have gotten this far:
n + d = 3.40
is that right? This question is from textbook Elementary and Intermediate Algebra

Found 3 solutions by checkley71, funmath, Earlsdon:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
N+D=43 & 5N+10D=340
N=43-D
5(43-D)+10D=340
215-5D+10D=340
5D=340-215
5D=125
D=125/5
D=25 NUMBER OF DIMES
N+25=43
N=43-25
N=18 NUMBER OF NICKELS
PROOF
5*18+10*25=340
90+250=340
340=340

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
This word problem has to do with coins, but I need to solve it by setting up and solving a system of two linear equations in two variables.
Cindy has 43 coins consisting of nickels and dimes. The total value of the coins is $3.40. How many coins of each kind does she have?
:
I like to do these in terms of cents to avoid decimals.
Let number of nickles be:n
Let the number of dimes be:d
When we add the coins together we have 43 coins: n+d=43
Nickels are worth 5 cents, so the amount of money in nickels we have is: 5n
Dimes are worth 10 cents: 10d
Total cents when added together: 5n+10d=340
:
E1: n+d=43
E2: 5n+10d=340
Solve E1, for one of the variables like d and substitute into E2 and solve for n.
:
E1: n+d=43 --> d=43-n
5n+10(43-n)=340
5n+430-10n=340
-5n+430=340
-5n+430-430=340-430
-5n=-90
-5n/-5=-90/-5
n=18
Substitute that into E1 to see how many dimes there were:
d=43-18
d=25
There were 18 nickels and 25 dimes.
Sanity Check: does 18 nickels and 25 dimes = $3.40? You decide if we're right.
Happy Calculating!!!

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Er...not quite!
Let n = the number of nickels ($0.05) and d = the number of dimes ($0.10).
The sum of the nickels and dimes (coins) can be written:
1) n + d = 43
The total value of the coins can be written:
2) n($0.05) + d($0.10) = $3.40
This is the required system of two equations in two unknowns (n and d).
You can solve this system by substitution.
Solve equation 1) for n: (n = 43 - d) and substitute this into equation 2) then solve for d.
2a) (43-d)($0.05) + d($0.10) = $3.40 Simplify and solve for d.
2.15 - 0.05d + 0.10d = 3.40
2.15 + 0.05d = 3.40 Subtract 2.15 from both sides.
0.05d = 1.25 Divide both sides by 0.05
d = 25 There are 25 dimes.
n = 43 - d
n = 43 - 25
n = 18 There are 18 nickels.
Check:
n + d = 18 + 25 = 43
18($0.05) + 25($0.10) = $0.90 + $2.50 = $3.40