jim has only dimes and nickels in his coin bank. he has 37 coins with a total value of $2.65. how many…

Explanation:

Step1: Set up equations

Let $x$ be the number of nickels and $y$ be the number of dimes. We have two - equations: $x + y=37$ (total number of coins) and $0.05x + 0.1y=2.65$ (total value of coins). From the first equation, we can express $y = 37 - x$.

Step2: Substitute $y$ into the second equation

Substitute $y = 37 - x$ into $0.05x+0.1y = 2.65$. We get $0.05x+0.1(37 - x)=2.65$.

Step3: Expand and simplify the equation

Expand the left - hand side: $0.05x+3.7−0.1x = 2.65$. Combine like terms: $0.05x-0.1x=2.65 - 3.7$. So, $-0.05x=-1.05$.

Step4: Solve for $x$

Divide both sides of the equation $-0.05x=-1.05$ by $-0.05$. We have $x=\frac{-1.05}{-0.05}=21$.

Answer:

21