Let us say that:
a = ones
b = fives
c = twenties
So that the total money is:
1 * a + 5 * b + 20 * c = 229
=> a + 5b + 20c = 229 -->
eqtn 1
We are also given that:
c = a – 5 -->
eqtn 2
a + b + c = 30 -->
eqtn 3
Rewriting eqtn 3 in terms of b:
b = 30 – a – c
Plugging in eqtn 2 into this:
b = 30 – a – (a – 5)
b = 35 – 2a -->
eqtn 4
Plugging in eqtn 2 and 4 into eqtn 1:
a + 5(35 – 2a) + 20(a – 5) = 229
a + 175 – 10a + 20a – 100 = 229
11a = 154
a = 14
So,
b = 35 – 2a = 7
c = a – 5 = 9
Therefore there are 14 ones, 7 fives, and 9 twenties.
For AD:
AD=root((c-0)^2 + (d-0)^2)=root((c)^2 + (d)^2)
For BC:
BC=root(((b+c) - b)^2+(d-0)^2)=root((c)^2+(d)^2)
For AB:
AB=root((b-0)^2 + (0-0)^2)=root((b)^2 + (0)^2)=root((b)^2)
For CD:
CD=root((c-(b+c))^2 + (d-d)^2)
CD=root((b)^2 + (0)^2)
CD=root((b)^2)
In one turn of the wheel, you will move the circumference of the wheel. To find the circumference, you just do π × diameter, so π × 34 = 106.8 inches. In 5 turns, you will just go 5 times the circumference, so you multiply by 5 to get 534.1 inches. I hope this helps!
