The solution is n = 5 and r = 4
Step-by-step explanation:
Given,
nCr : (n+1)Cr : (n+2)Cr = 1:3:7
To find the value of n and r.
Formula
nCr = 
[ n! means = n.(n-1).(n-2)....3.2.1]
Now,
nCr : (n+1)Cr = 1:3 and (n+1)Cr : (n+2)Cr = 3:7
or, : 
= 1:3 or, : 
= 
or, × 
= 
or, ×
=
or, 
= or, 
=
or, 3(n+1-r) = n+1 or, 7(n+2-r) = 3(n+2)
or, 3n+3-3r = n+1 or, 7n+14-7r = 3n+6
or, 2n-3r = -2 or, 4n-7r = -8
Now, by solving
2n-3r = -2 -----(1)
4n-7r = -8 -----(2) we will get n and r
Multiplying (1) by and then subtract with (2) we get,
2(2n-3r) - (4n-7r) = -4-(-8)
or, 4n-6r-4n+7r = 4
or, r = 4
From (1) we get,
2n = -2+3(4)
or, 2n = 10
or, n = 5
Hence,
n = 5 and r = 4
So his lawn can be divided into 4 shapes: 1 rectangle, 2 triangles, and an irregular shape. So you get the area of the rectangle which is 48*120=5,760.
For the part above the rectangle, you can see that the 2 triangles and the irregular shape make one large triangle so take the area of that. (I’m going to refer to this as the BIG triangle).
.5*40*120=2,400
The base of the triangle is equal to the base of the rectangle. The height of the triangle you get by subtracting the height of the WHOLE lawn by the height of the rectangle. (88-48=40).
Inside that large triangle made up of three shapes, you can see another triangle that’s made up of one triangle and the irregular shape. I’ll refer to this triangle as triangle 1.
Take the area of that triangle.
.5*25*75=937.5
The base of the triangle you get by adding the base of the smaller triangle and the irregular shape. (51+24=75)
Inside the triangle you just took the area of (triangle 1) is another triangle (which I’ll refer to as triangle 2). Take the area of triangle 2.
.5*51*17=433.5
Subtract the area of triangle 1 by the area of triangle 2 and that’ll give you the area of the irregular shape.
937.5-433.5=504
So now you add the areas of the BIG triangle and the rectangle.
5760+2,400=8160
Make sure you subtract the irregular shape since it isn’t part of the lawn’s area.
8160-504=7656
So the lawn is 7656 square feet. Multiply it by .005. That equals 38.28. That’s how much fertilizer he needs to use.
Multiply 1.25 to 38.28 to get the amount of money he needs to spend.
47.85 dollars
I might’ve made a few mistakes but I hope my reasoning was at least understandable
The rate of change is 3 hope this helps
