Respuesta :
Answer:
Number of dims in the bank are 10. Â Â Â Â Â Â Â Â Â
Step-by-step explanation:
Given : ​Michael's bank contains only​ nickels, dimes, and quarters. There are 64 coins in​ all, valued at ​$5.30. The number of nickels is 8 short of being three times the sum of the number of dimes and quarters together.
To find : How many dimes are in the​ bank?
Solution :
Let number of nickels = x
Number of dims = y
Number of quarters = z
Total there are 64 coins.
i.e. [tex]x+y+z=64[/tex] ....(1)
The cost of nickels = $0.05
The cost of dims = $0.10
The cost of quarters = $0.25
Total value at $5.30.
i.e. [tex]0.05x+0.10y+0.25z=5.30[/tex] .....(2)
The number of nickels is 8 short of being three times the sum of the number of dimes and quarters together.
i.e. [tex]x=3(y+z)-8[/tex] .....(3)
Substitute y+z from (1),
[tex]x=3(64-x)-8[/tex]
[tex]x=192-3x-8[/tex]
[tex]4x=184[/tex]
[tex]x=46[/tex]
Substitute the value of x in (1) and (2),
[tex]46+y+z=64[/tex]
[tex]y+z=18[/tex] .....(4)
[tex]0.05(46)+0.10y+0.25z=5.30[/tex]
[tex]2.3+0.10y+0.25z=5.30[/tex]
[tex]0.10y+0.25z=3[/tex]
[tex]10y+25z=300[/tex] Â .....(5)
Solving equation (4) and (5),
Substitute the value of y from (4) in (5),
[tex]10(18-z)+25z=300[/tex]
[tex]180-10z+25z=300[/tex]
[tex]15z=120[/tex]
[tex]z=\frac{120}{15}[/tex]
[tex]z=8[/tex]
Substitute the value of z in (4),
[tex]y+8=18[/tex]
[tex]y=10[/tex]
So, Number of nickels are x=46
Number of dims are y=10
Number of quarters are z=8.
Therefore, Number of dims in the bank are 10.
