Question

If a cow eats 50 pounds of grass every day EXCEPT every 5th day on which it only eats 40 pounds of grass. If the cow continues this, how many pounds of grass will it eat in 222 days? The cow will eat 10,660 pounds of grass in 222 days

Answer 1

SOLUTION

GIVEN

A cow eats 50 pounds of grass every day EXCEPT every 5th day on which it only eats 40 pounds of grass.

TO DETERMINE

If the cow continues this, how many pounds of grass will it eat in 222 days

EVALUATION

The cow eats 50 pounds of grass every day EXCEPT every 5th day on which it only eats 40 pounds of grass

So the cow eats 40 pounds of grass on every 5th day

We have to find the amount of grass will it eat in 222 days

Which gives the cow eats 40 pounds of grass on 5th , 10th , 15th , 20th , 25th , ... , 215th , 220th

This is an arithmetic progression with

First term = a = 5

Common Difference = d = 5

Let 220 is the nth term of the AP

So we have

$\sf{a + (n - 1)d = 220}$

$\sf{ \implies \: 5 + 5(n - 1)= 220}$

$\sf{ \implies \: 5(1 + n - 1)= 220}$

$\sf{ \implies \: 5n = 220}$

$\sf{ \implies \: n = 44}$

So total number of 5th days = 44

Total number of days except 5th days

= 222 - 44

= 178

Hence the required amount of of grass will it eat in 222 days

$\sf{ = (44 \times 40) + (178 \times 50) \: \: \: pounds}$

$\sf{ = (1760 + 800) \: \: \: pounds}$

$\sf{ = 10660 \: \: \: pounds}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Using brackets, write 2 pairs of numbers whose sum is 12. Write one equality using

the...

https://brainly.in/question/38147943

2. use the following rational numbers to frame an example of distributive property of multiplication over addition for ratio...

https://brainly.in/question/38849015