Bob has 18 coins, both dimes and nickels, worth $1.45. How many of each coin does he have?

Dimes: 11, Nickels: 7

Step-by-step explanation:

Let's say the number of dimes ⇒ x and the number of nickels ⇒ y:

We know the total number of coins, 18, such that we can format one equation to be:

x + y = 18

We also know the total cost of dimes and nickels, 1.45 dollars. Here we (in general) know that the cost of a dime is 0.1 dollars and the cost of a nickel is 0.05 dollars so that 0.1x represents the total cost of dimes if x represents any number, and 0.05y represents the total cost of nickels if y represents any number. Knowing this, let us format another equation to be:

0.1x + 0.05y = 1.45

So, we now have two equations:

x + y = 18, and

0.1x + 0.05y = 1.45

Let's alter the first equation as such, so that x is isolated:

x + y = 18

x = 18 - y

Now let's substitute the this value of x in the second equation and solve for y:

0.1x + 0.05y = 1.45

0.1 (18 - y) + 0.05y = 1.45

1.8 - 0.1y + 0.05y = 1.45

1.8 - 0.05y = 1.45

-0.05y = - 0.35

y = 7 nickels

Knowing the number of nickels, substitute the value of y into the first equation:

x + y = 18

x + (7) = 18

x = 11 dimes