Question

Julie is throwing a surprise birthday party for her friend. She wants to spend no more than $35. 00 on decorations. At a local party store, she can buy helium-filled balloons for $2. 50 each and rolls of streamers for $3. 50 per roll. Let x represent the number of balloons purchased and y be the number of rolls of streamers. The inequality 2. 50x +3. 50y<=35. 0. Determine how many of each type of decoration she can buy. If Julie wants to buy 6 balloons, how many rolls of streamers can she buy without going over budget?

Answer 1

Explanation:

The inequality that represents Julie's budget constraint is:

2.50x + 3.50y ≤ 35.00

Where:

x = number of helium-filled balloons

y = number of rolls of streamers

To determine how many of each type of decoration Julie can buy, we can plug in different values for x and solve for y. However, we need to keep in mind that both x and y must be non-negative integers since they represent quantities of balloons and rolls of streamers.

Let's start by solving for y when x = 6 (Julie wants to buy 6 balloons):

2.50(6) + 3.50y ≤ 35.00

15 + 3.50y ≤ 35.00

3.50y ≤ 20.00

y ≤ 20.00 / 3.50

y ≤ 5.71

Since y must be a whole number, Julie can buy a maximum of 5 rolls of streamers without going over budget when she buys 6 balloons.

Therefore, Julie can buy 6 balloons and 5 rolls of streamers without exceeding her budget of $35.00.