If Andy has 102 coins mixed with dimes and quarters and monetary value of $17.10 then he has 56 dimes and 42 quarters.
Given number of coins Andy has is 102 and montary value of all coins is $17.10.
We have to determine number of dimes and quarters.
1 dime=$0.10
1 quarter=$0.25
Suppose the number of dimes be x and number of quarters be y.
The equations are:
0.10x+0.25y=17.10------------1
x+y=102-------------2
from equation 2, y=102-x
Put the value of y=102-x in equation 1
0.10x+0.25(102-x)=17.10
0.10x+25.5-0.25x=17.10
-0.15x=17.10-25.5
-0.15x=-8.4
x=8.4/0.15
x=56
Put the value of x in y=102-x
y=102-56
y=46
Hence Andy has 56 number of dimes and 46 quarters.
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