This problem can be solved by the chicken rabbits method or you can just do simple algebra.
I.) Chicken and rabbits method
First assume all 110 coins are dimes and none are quarters.
We will have a total value of 11 dollars
Now for each dime we switch out for a quarter, we adds 15 cents to the total value.
18.50-11=7.50 dollars
There are 750/15=50 group of 15 cents in the 7 dollars and 50 cents.
This also meant that we need to switch out 50 dimes for 50 quarters.
So we have 50 quarters.
That first method is very good and very quick once you get the hang of it, now I'm going to show you the algebraic way to solve this.
Let's say there are x dimes and y quarters.
Set up equation
x+y=110
10x+25y=1850
Now solve multiply first equation by 10
10x+10y=1100
subtract
15y=750
y=50
Now we set the numbers of quarters to y so the answer is 50 quarters.
I personally recommend using algebra whenever you can because the practice is very important and you will eventually get really fast at setting up and solving equations. The first method is faster in this case but the second is more generalize, hope it helps.
X-12 will give the other number
we have
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
remember that
Square root both sides
Simplify
therefore
<u>the answer is</u>
The length of the longer base is 41 ft.
<u><em>Explanation</em></u>
Lets assume, length of one base is ft.
As, another base is 19 less than five times the length of this base, so the length of another base
The trapezoid has a height of 18 ft and area of 477 ft²
Formula for Area of trapezoid, , where = Two bases of trapezoid and = height of the trapezoid.
Given in the question: and
We have also two bases as: and
So, according to the above formula...
So, length of one base is and another base
That means, the length of the longer base is 41 ft.
The nearest whole number is 20.