Question

The rodent control task force went into the woods one day and caught 200 rabbits and 18 squirrels. The next day they went into the woods and caught three fewer rabbits and two more squirrels than the day before. Each day they went into the woods and caught three fewer rabbits and two more squirrels than the day before. This continued through the day when they caught more squirrels than rabbits. Up through that day how many rabbits did they catch in all? I NEED HELP ASAP PLS!! WILL MARK BRAINLIEST IF CORRECT

Answer 1

Answer:

6068 rabbits

Step-by-step explanation:

Given

$Rabbits = 200$

$Reduction = 3\ daily$

$Squirrels = 18$

$Increment = 2\ daily$

Required

Determine number of rabbits caught up till the day when they caught more squirrel.

Let the number of days be n

On any n day,

The number of rabbits they catch is:

$Rabbit = 200 - 3n$

The minus symbol is used because there's a reduction in the numbers of Rabbit caught, each day.

The number of squirrel they catch is:

$Squirrel = 18 + 2n$

The addition symbol is used because there's an increment in the numbers of Squirrel caught, each day

First, we need to solve for n

The expression when they catch more rabbits than squirrel is:

$Squirrel > Rabbit$

Substitute values for Squirrel and Rabbit

$18 + 2n > 200 - 3n$

To solve the above expression, we start by collecting like terms

$2n + 3n > 200 - 18$

$5n > 182$

Solve for n

$n > \frac{182}{5}$

$n > 36.4$

Days must be an integer. So, we have to round the above value.

$n > 36$

The above expression shows that they caught more squirrel on a day greater than 36.

This day is 37.

i.e.

$n = 37$

The reduction in the number of rabbits daily is an indication of Arithmetic progression.

So, to calculate the number of rabbits caught up till the day when they caught more squirrel, we make use of Sum of n terms of an AP using:

$S_n = \frac{n}{2}(2a + (n-1)d)$

In this case:

$n = 37$

a = Initial Number of rabbits;

$a = 200$

d = the reduction (common difference)

$d = -2$

Substitute these values in the given formula:

$S_n = \frac{n}{2}(2a + (n-1)d)$

$S_{37} = \frac{37}{2}(2 * 200 + (37 - 1) * -2)}$

$S_{37} = \frac{37}{2}(2 * 200 + 36 * -2)}$

$S_{37} = \frac{37}{2}(400 -72)}$

$S_{37} = \frac{37}{2} * 328$

$S_{37} = 37 * 164$

$S_{37} = 6068$

Up till that day, the number of rabbits is 6068