# A coin collector has $1.70 in dimes and nickels. She has 2 more dimes than nickels. How many nickels does she have? ##### 1 Answer Aug 9, 2016 10 nickels and 12 dimes #### Explanation: Given that 1 nickel $\to$5 cents 1 dime $\to$10 cents 100 cents $\to$1 dollar So 2 nickels is 1 cent Let the count of nickels be $n$Let the count of dimes be $d$Known that$1.70 $\to$ 1.70xx100 = 170 cents
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So $5 n + 10 d = 170$..........................Equation(1)

It is given that there is 2 more dimes than nickels giving:

$d = 2 + n$...Equation(2)

Using equation(2) substitute for d in equation(1)

$5 n + 10 \left(2 + n\right) = 170$

$5 n + 10 n + 20 = 170$

Subtract 20 from both sides

$15 n = 150$

Divide both sides by 15

$n = \frac{150}{15} = 10$
$\textcolor{g r e e n}{\text{So there are 10 nickels}}$

Thus equation (2) becomes$d = 2 + n \to d = 2 + 10 = 12$

$\textcolor{g r e e n}{\text{So there are 12 dimes}}$
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Check $\text{10 nickels"color(white)(..)-> 10xx5color(white)(.)" cents"=color(white)(.)50" cents}$
$\text{ 12 dimes "color(white)(.)->12xx10" cents"=120" cents}$

$= 170 \text{ as required}$