Answer: 23 dimes & 7 quarters
Step-by-step explanation:
You can create two equations:
[tex]\left \{ {{x + y = 30} \atop {0.10x + 0.25y =4.05}} \right.[/tex]
Rearrange x + y = 30:
[tex]y=30-x[/tex]
Substitute it into the x-value of the other equation & solve:
[tex]0.10x + 0.25y =0.10x + 0.25(30-x)=4.05\\0.10x+7.5-0.25x=4.05\\0.10x-0.25x=4.05-7.5\\-0.15x=-3.45\\x=\frac{-3.45}{-0.15} =23[/tex]
With the x-value, substitute it back to the original equation to find y-value:
[tex]y=30-x=30-23=7[/tex]
Therefore, there are 23 dimes & 7 quarters.
There are 23 dimes and 7 quarters.
Given that, the total number of coins=30.
To convert dimes to dollars we need to multiply the number of dimes by 0.1.
Let the number of dimes be x, and then the number of quarters will be 30-x.
Now, x×0.1+(30-x)×0.25=4.05
⇒-0.15x=-3.45
⇒x=23
30-x=7
Hence, there are 23 dimes and 7 quarters.
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