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K, so I have this math problem that I have absolutely have NO clue how to do it. It’s an inequalities problem I think.
Jo has 37 coins(nickels, dimes and quarters) equaling up to $5.50. She has four more quarters than nickels.
How many dimes does she have?
Can someone please help me?? I’m really stuck!!!!
# P T
nickels x 5 5x
dimes 37-(x+x+4) 10 10(37-x+x+4)
quarters x+4 25 25(x+4)
5x+10(37-x+x+4)+25(x+4)=5.50
I hope that helps…that’s about all I remember 🙂
I don’t know why its not staying in chart form, sorry!
Let x=number of nickels
Then x+4=number of quarters
So the number of dimes would be:
37-x-(x+4)=
37-2x-4=
33-2x —- is the number of dimes
(lets deal in pennies)
5x+25(x+4)+10(33-2x)=550
so 5x+25x+100+330-20x=550
collect like terms
10x+430=550
subtract 430 from each side
10x+430-430=550-430=
10x=120
divide each side by 10
x=12
number of nickelsx+4=12+4=16
number of quarters33-2x=33-24=9
number of dimesCheck
5*12=60
25*16=400
9*10=90
60+400+90=550
550=550
Just google the question and a whole list of explanations come up. the answer is 9 dimes.
Here you go:
Set the number of nickels as “n”, the number of dimes as “d”, and the number of quarters as “q”.
There are a total of 37 coins. Therefore:
n+d+q=37
You also know that the total in dollar amounts is equal to $5.50. Therefore:
.05n+.10d+.25q=5.50
In the first equation, we can set q = n+4 (as there are 4 more quarters than nickels). Resetting the first equation:
n+(n+4)+d=37
Solve for “d” in terms of “n”:
d=33-2n
Now we set the second equation (using q=n+4):
.05n+.10d+.25(n+4)=5.50
Now you can plug the “d=33-2n” value to the above equation to solve for “n”:
.05n+.10(33-2n)+.25(n+4)=5.50
Do all the annoying math, and the final answer is n=12. That gives you the number of nickels. Finally:
#n=12
#q=16
#d=37-28=9
and that’s your answer! Double check your work and make sure the math is right:
.05(12)+.1(9)+.25(16)=5.5
Hope that answers your question! Just keep in mind the moral of the equation: if you have multiple variables (like you do here), you need to set up equations to solve for a variable in terms of a main variable – which in this case I made “n” as our main variable.
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