Question

Kelvin is having a party and has invited 24 friends. He plans to purchase sodas that cost $5.00

for a 12-pack and chips that cost $3.00 per bag. He wants each friend to have at least two sodas. Kelvin's

budget is $35.00. Use the system of linear inequalities below to represent this situation.

5x + 3y = 35

x 24

Answer 1

The required system of inequality would be,

5x + 3y ≤ 35, x ≥ 4, y ≥ 0

Explanation:

Let x be the number of packs of 12 sodas and y be the number of bags of chips

∵ Each pack of 12 sodas costs $ 5.00 and each bag of chips costs $ 3.00

So, the total spending = ( 5x + 3y ) dollars,

Now, according to the question,

Total budget is $ 35.00

`\implies 5x + 3y \leq 35`

Again,

Number of friend = 24,

Also, least number of sodas for each friend = 2 × number of friends = 2 × 24 = 48,

One pack of soda = 12 sodas

⇒ 1 soda = 1/12 packs of sodas

⇒ 48 sodas = 4 packs of sodas

So, number of packs of sodas ≥ 4

⇒ x ≥ 4

Since, number of bags can not negative ⇒ y ≥ 0