Answer:
There are 5 cats and 6 children
Step-by-step explanation:
Let x = number of cats
Let y= number of children
Counting heads gives 11
X+Y = 11 .....eq1
Counting feet gives 32
Cats has 4legs,child has 2 legs
4X + 2Y=32 ....eq2
X = 11 - Y
Put in eq2
4(11-Y) + 2Y = 32
44 - 4Y + 2Y=32
12=2Y
Y=12/2=6
Y=6= Children
Put Y=6 in eq2
X + 6=11
X=11-6=5
X= 5 = cats
<h3>________________________________________________</h3>
Step-by-step Solution for Part-a:
<u>We know that:</u>
- Row-1: 20 seats
- Row-2: 20 + 11
- Row-x: 20 + (11x - 11)
Since the number of rows in rows x is 20 + (11x - 11), the formula to calculate the number of seats in each row is 20 + (11x - 11).
<h3>________________________________________________</h3>
Step-by-step Solution for Part-b:
<u>We know that:</u>
- y rows = 174 seats
- Obtained rule from part-a: 20 + (11y - 11)
<u>Solution:</u>
- 20 + (11y - 11) = 174 rows
- => 20 + 11y - 11 = 174 rows
- => 9 + 11y = 174 rows
- => 11y = 174 - 9 rows
- => 11y = 165
- => y = 165/11
- => y = 15
Hence, the row which has 174 seats is row 15.
<h3>________________________________________________</h3>
2370 / (2/5) = x / 1...2370 to 2/5 = x to 1
cross multiply
(2/5)(x) = (2370)(1)
2/5x = 2370
x = 2370 * 5/2
x = 11850/2 = 5925 <== their entire goal
Let the two numbers be x and y
As given, the difference of two numbers is 3, so
or
....(1)
And their sum is 25, so
.....(2)
Putting x=3+y in equation (2)



As, x+y=25


So the two numbers are = 14 and 11