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Ryan has some nickels and dimes. Altogether, he has 34 coins that total $2.60. Write the system of equations to determine how many of each coin he has.

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djcatmaster007p6qv2j
8 dimes is $1.80 while 16 nickels is $0.80 or 80 cents. This total is in fact $2.60.
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In the question, it is given that

Ryan has some nickels and dimes. Altogether, he has 34 coins that total $2.60.

Let the number of nickels be n and number of dimes be d.

So we have

[tex] n+d =34 \\
0.05n + 0.1d = 2.6 [/tex]

Multiplying first equation by -0.05 and add it to second equation, we will get

[tex] -0.05n -0.05d +0.05n +0.1d = -1.7+2.6 [/tex]

[tex] 0.05d = 0.9
\\
d = 18 [/tex]So number of Dimes are 18 and number of nickels are

[tex] 34-18=16 [/tex]

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