Question

each afternoon maria walks the dogs at a local pet shelter for up to 2 hours. maria spends 16 minutes walking a large dog and 12 minutes walking a small dog. write an inequality for this situation. if maria walked 9 dogs in one afternoon, what is the greatest number of large dogs that she could have walked that afternoon?

Answer 1

`16x + 12y\leq 120` is the inequality that represents this situation

The greatest number of large dogs that she could have walked that afternoon is 3

Solution:

Each afternoon maria walks the dogs at a local pet shelter for up to 2 hours

Maria spends 16 minutes walking a large dog and 12 minutes walking a small dog

To find: Inequality for this situation

Let "x" be the number of large dogs taken for walking

Let "y" be the number of small dogs taken for walking

Total time spend = 2 hours = 120 minutes

Time spent for large dog = 16 minutes

Time spent for small dog = 12 minutes

Therefore, a inequality is framed as:

number of large dog x Time spent for large dog + number of small dogs x Time spent for small dog
`\leq` Total time spend

`x * 16 + y * 12\leq 120\\\\16x + 12y\leq 120`

Here we used "less than or equal to" , since total time spend is up to 2 hours

Thus the inequality is found

If maria walked 9 dogs in one afternoon, what is the greatest number of large dogs that she could have walked that afternoon?

So total dogs = 9

number of large dogs + number of small dogs = 9

x + y = 9

y = 9 - x --- eqn 1

Substitute eqn 1 into inequality

`16x + 12(9-x)\leq 120\\\\16x + 108-12x\leq 120\\\\4x\leq 12\\\\x\leq 3`

Thus the greatest number of large dogs that she could have walked that afternoon is 3