A collection of 52 dimes and nickels is worth $4.50. How many nickels are there?

alexmjn

alexmjn

Answered question

2022-09-03

A collection of 52 dimes and nickels is worth $4.50. How many nickels are there?

Answer & Explanation

Carleigh Tate

Carleigh Tate

Beginner2022-09-04Added 8 answers

d= dimes, n= nickles
so, 52=n+d
and 4.50=.10d+.05n
solve for n in second equation and plug that value in for n inthe first equation
4.5=.1d+.05n multiply both sides by 20
90=2d+1n
n=90-2d
so plug this into 52=n+d and you get
52=90-2d+d and solve for d
you get d=38 plug this back into 52=n+d and you get
n=14
check your answer
52= (14)+(38) correct
4.5=.1(38)+.05(14) correct
so your answer is 38 dimes and 14 nickles
onthewevd

onthewevd

Beginner2022-09-05Added 1 answers

One way to solve is using a system of equations.
Let n = # of nickels
d = # of dimes
so we know: n + d = 52, since there are 52 coins total.
We also now that .05n + .10d = 4.50, since the total value is$4.50
You can multiply through by 100 to get rid of decimals.
n + d = 52
5n + 10d = 450
Use addition/elimination to solve. Multiply the top equation by - 5
-5n - 5d = -260
5n + 10d = 450
Add together
5d = 190
d = 38
Since n + d = 52 and d = 38, n = 14
14 nickels and 38 dimes.

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