Studdy AI Logo
Math  /  Algebra

Question12 more practice 5) Pet Supplies makes a profit of $5.50\$ 5.50 per bag on its line of natural dog fe 5 sions to nn profit of no less than $5225\$ 5225, how many bags of dog food does it need to sell?

Studdy Solution

STEP 1

What is this asking? How many bags of dog food need to be sold to make at least $5225\$5225 if each bag earns $5.50\$5.50 profit? Watch out! Don't forget, we're looking for a *minimum* number of bags, not an exact amount!

STEP 2

1. Set up the inequality
2. Solve for the number of bags

STEP 3

Let nn be the number of bags of dog food Pet Supplies needs to sell.
This is our **mystery number** that we're trying to find!

STEP 4

The profit per bag is $5.50\$5.50.
So, the **total profit** from selling nn bags is 5.50⋅n5.50 \cdot n.

STEP 5

We want the **total profit** to be *no less than* $5225\$5225, which means it should be greater than or equal to $5225\$5225.
So, our inequality is: 5.50⋅n≥5225 5.50 \cdot n \ge 5225

STEP 6

To find the **number of bags**, we need to isolate nn.
We can do this by dividing both sides of the inequality by **5.50**.
Remember, we're dividing by a positive number, so the inequality sign *stays the same*! 5.50⋅n5.50≥52255.50 \frac{5.50 \cdot n}{5.50} \ge \frac{5225}{5.50}

STEP 7

Now, we simplify!
On the left side, the 5.505.50 in the numerator and denominator divide to one, leaving just nn.
On the right side, we perform the division: n≥52255.50 n \ge \frac{5225}{5.50} n≥950 n \ge 950

STEP 8

Pet Supplies needs to sell at least **950** bags of dog food to reach their profit goal.
Woof woof!

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord