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Patty has 44 coins, all nickels, dimes and quarters, worth a total of $6.45. She has 3 times as many dimes as nickels. Set up an equation in terms of only one variable and then solve it to find the number of each type of coin she has

Respuesta :

Answer: There are 7 nickles, 21 dimes and 16 quarters.

Step-by-step explanation:

Since we have given that

Number of coins = 44

Let the number of nickels be 'x'.

Let the number of dimes be '3x'.

Let the number of quarters be

[tex]44-(x+3x)\\\\=44-4x[/tex]

According to question, we get

[tex]0.05x+0.10(3x)+0.25(44-4x)=6.45\\\\0.05x+0.3x+11-x=6.45\\\\-0.65x=6.45-11\\\\-0.65x=-4.55\\\\x=\dfrac{4.55}{0.65}\\\\x=7[/tex]

So, there are 7 nickles,

3x =[tex]3\times 7=21[/tex]

[tex]44-4x=44-4\times 7=44-28=16[/tex]

Hence, there are 7 nickles, 21 dimes and 16 quarters.

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