Gina has a collection of nickels and dimes worth $8.65. If she has 101 total coins, how many dimes does Gina have?

Gina have 72 dimes.

Step-by-step explanation:

We know nickel is made up of  5 cents and dimes is made up of  10 cents. so we could write the equation.

0.05x + 0.10y = 8.65   where x is th number of nickels and y is the number of dimes.

We could also write another equation to represent the total coins.Since the coins are only nickels and dimes we could say that   x+y = 101 which means the total number of nickels x and the total number of dimes y has to equal 101.

0.05x + 0.10y = 8.65   solve both system of equation using the elimination

x + y =  101                     method

multiply the down equation by -0.05 to eliminate the x variables.

-0.05(x+y) = 101(-0.05)  

-0.05x - 0.05y = -5.05  

NOw we have a new equation so you could add them up and eliminate the x terms.

0.05x + 0.10y =8.65

-0.05x  - 0.05 = -5.05

   0   +   0 .05y = 3.6

                   y= 72  

Now we know that Gina has 72 dimes and since we know the total subtract it to find how many nickels.

101 - 72 = 29

Let's start this problem by setting up a chart.

The chart is attached below.

Down the left side, you have your different types

of coins, in this case, nickels and dimes.

Across the top of the chart, we will use our total value formula.

number of coins · value of each coin = total value

Since Gina has a total of 101 nickels and dimes,

in the first column of our chart we can represent

her number of nickels as x and her number of dimes as 101 - x.

In the second column, we have the value of a nickel

which is 5 cents and the value of a dime, 10 cents.

To fill our the 3rd column in your chart, multiply

the information in the first two columns together.

So the total value of our nickels is x · 5 or 5x and

the total value of our dimes is 101 - x · 10 or 10(101 - x).

You will always use the information in the last column of your chart,

the total value column, to setup the equation.

If you look back up at the original problem,

the total value of all the coins is $8.65.

That means that the total value of the nickels

plus the total value of our dimes is $8.65.

Solving the equation from here, you'll find that x = 29.

I have showed my work in the image attached.

Going back up into our chart, you'll see that x

represents the number of nickels that Gina has.

So Gina has 29 nickels.

We can find the number of dimes by using the box below the nickels.

Here, we have 101 - x.

Since x is 29, we have 101 - 29 which is 72.

So Gina has 72 dimes.

-18 degrees is the answer : )