Ian has 30 nickels and dimes worth $2.40 in his book bag. How many nickels and dimes does he have

Answer 1

This question can be expressed in an algebraic equation, where x is equal to the amount of nickels and y is equal to the amount of dimes.

In other words, x = amount of nickels and y = amount of dimes.

Each nickel is worth .05 dollars, and each dime is worth .10 dollars.

To find out how much money in nickels or dimes he has, you would multiply the number of dimes/nickles by the amount each one is worth. You would then add the amount of money you'd get from each separate kind of currency to get the total amount.

Therefore, given that our total known amount is $2.40, our equation looks like this:

2.40 = x(.05) + y(.10)

The word problem states that we have a total of 30 coins, therefore we can state this as a separate algebraic equation, x + y = 30

We can try to solve this equation for one of our variables. Let's choose x.

We need to get x on it's own on one side of the equation, so we will subtract y from both sides. This makes our equation:

x = 30 - y

Now we can replace the x in our original equation with our answer for x, here.

2.40 = x(.05) + y(.10)

2.40 = (30-y)(.05) + y(.10)

We have to now multiply 30-y by .05 to simplify

2.40 = 1.5 - y(.05) + y(.10)

We can now add the two variables that are multiplied by y. -.05 plus .10 is equal to .05

2.40 = 1.5 + y(.05)

Now we get y by itself by subtracting 1.5 from both sides and then dividing both sides by .05

.9 = y(.05)

y = 18

We now know we have 18 dimes.

We now go back to our second equation, 30 = x + y and plug in our answer for y

x + 18 = 30

30 - 18 = x

12 = x

We now know we have 12 nickels.

To check, plug in your answers in the original equation.

12(.05) + 18(.10) = .6 + 1.8 = 2.40

Our answers were right, tada!