Respuesta :
Answer:
4 nickels
12 dimes
Step-by-step explanation:
Dimes are worth .1 each while nickels are .05 each.
We have 8 more dimes than nickels. Let d represent number of dimes and n for number of nickels. This means we have d=8+n.
If all our nickels and dimes together are worth 1.4 then we have another equation .1d+.05n=1.4
Lets put our equations together:
d=8+n
.1d+.05n=1.4
‐-----------------Plug first equation into second.
.1(8+n)+.05n=1.4
Distribute
.8+.1n+.05n=1.4
Combine like terms
.8+.15n=1.4
Subtract .8 on both sides
.15n=.6
Divide both sides by .15
n=.6/.15=4
Remember there are 8 more dimes so d=8+4=12.
This question is solved using a system of equations. I am going to say that:
- x is the number of dimes.
- y is the number of nickels.
Doing this, we get that: There are 4 nickels and 12 dimes.
There are 8 more dimes than nickels in the bank.
This means that: [tex]y = x + 8[/tex]
There is a total of $1.40.
- Nickel is worth $0.05.
- Dime is worth $0.1.
Thus, for the nickels:
[tex]0.05x + 0.1y = 1.4[/tex]
Since [tex]y = x + 8[/tex]
[tex]0.05x + 0.1(x + 8) = 1.4[/tex]
[tex]0.05x + 0.1x + 0.8 = 1.4[/tex]
[tex]0.15x = 0.6[/tex]
[tex]x = \frac{0.6}{0.15}[/tex]
[tex]x = 4[/tex]
For the dimes:
[tex]y = x + 8 = 4 + 8 = 12[/tex]
There are 4 nickels and 12 dimes.
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