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A bag contains 23 coins consisting of dimes and nickels. The total value of the coins is $1.85. Write a system of equations and solve to find out how many dimes are in the bag.

A Bag Contains 23 Coins Consisting Of Dimes And Nickels The Total Value Of The Coins Is 185 Write A System Of Equations And Solve To Find Out How Many Dimes Are class=

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The number of dimes in a bag are required.

The number of dimes in the bag is 14.

Total value of coins is $1.85

Total number of coins is 23

Let number of dimes be [tex]x[/tex]

and number of nickels be [tex]y[/tex]

[tex]x+y=23[/tex]   [tex]\times0.05[/tex]

[tex]0.1x+0.05y=1.85[/tex]

[tex]0.05x+0.05y=1.15[/tex]

[tex]0.1x+0.05y=1.85[/tex]

Subtracting the equations

[tex]-0.05x=-0.7\\\Rightarrow x=\dfrac{0.7}{0.05}\\\Rightarrow x=14[/tex]

The number of dimes in the bag is 14.

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