Question

Penny is going to make a donation to our local animal shelter. The price of each item she will donate is shown.

so far she has 30 cans of cat food 34 cans of dog food and 18 bags of cat she wants the value of her donation to be more than $380 how many bags of dog food does Penny need to donate to meet her goal?

Answer 1

Second Choice: 8.73b + 171.48 > 381

Explanation:

This is a tricky question because the first two choices both represent an inequality that satisfy the conditions

First, let's eliminate obvious wrong choices.

If b represents the number of bags of dog food and one bag costs $8.73, there should be term 8.73b somewhere in the inequality since 8.73b represents the total $ cost of b bags of dog food.

This means we can eliminate the last two choices

Let's deal with the knowns and compute the dollar amounts of each of the products being donated

30 cans of cat food at $0.57 per can = 0.57 x 30 = $17.10

34 cans of dog food at $0.84 per can = 0.84 x 34 = $28.56

18 bags of cat food at $$6.99 per bag = 6.99 x 18 = $125.82

The sum of these is $171.48

She is also donating b bags of dog food at $8.73 per bag = 8.73 x b = $8.73b

So the total cost of the donation =
8,73b + 171.48 which has to exceed 381

So the inequality is
8.73b + 171.48 > 381

Which is the choice you have selected and I believe it is correct

Now, the tricky part comes because if you subtract 171.84 from both sides of the inequality we get

8.73b > 318 - 171.48

Both inequalities are equivalent but we would not write an inequality of the type where the RHS is a mathematical expression. We would instead simplify the right hand side and write it as

8.73b > 209.52 (381-171.48 = 209.52)

I believe the way the question is worded is the LHS should be the $sum of all the donations and the RHS the minimum value.

So the best choice is choice 2: 8.73b + 171.48 > 381

i hope that helps.