Dimes and quarters. total coins = 44 total value = $9.20 show work.

With that information we can form 2 equations where x = Total of dimes that person has and
y = Total of quarters he has :
x + y = 44. ( Equation represents that the total of coins he has is 44 )

10x + 25y = 920 ( Equation represents that each dime is worth 10 and eache quarter 25. And that the total of dimes and quarters he has sum to 920 )

Now we need to isolated one of the variables ( x and y ) to get their values and apply it to one of the equations to het the value pf the pther variable.

We can do that through the method of Elimination :
To do that we need first to set one of the variables equal in both of the equations :
Lets do it with x :

x + y = 44
10x + 25y = 920

Multiply the entire first equation by 10 so x in both equations are equal :

10x + 10y = 440
10x + 25y = 920

Now we can subtract one of the equation by the other :

1st equation - 2nd equation:
10x - 10x + 10y - 25y = 440 - 92010x - 10x cancel out so we end up with :
-15y = - 480
Now we just need to isolate y by dividing both sides of the equation by -15
-15/-15y = -480/-15
y = 32

2nd equation by the 1st equation :
10x - 10x + 25y - 10y = 920 - 440
15y = 480
y = 32

Now that we have the value of y , we can apply it to one of the equations to find the value of x :

y = 32

x + y = 44
x + 32 = 44

Shift 32 to the other side of the equation by subtracting 32 from both sides of the equation:

x + 32 - 32 = 44 - 32
x = 12

Awnser : x = 12 , y = 32
That person has 12 dimes and 32 quarters

I hope you understood my brief explanation, and please consider marking this awnser as Branliest if you think it deserves it. Thank you! :)