Question

Emma is having a slumber party for 12 of her friends. The menu includes hot wings and hamburgers. Wings will cost $0.45 per wing, and each complete hamburger will cost $1.75. If Emma can spend at most $90 at the grocery store, write the linear inequality in standard form that will represent this situation if x = the number of wings and y = the number of hamburgers.

a) 0.45x + 1.75y ≤ 90
b) 0.45x + 1.75y < 90
c) 0.45x + 1.75y = 90
d) 0.45x + 1.75y > 90

Answer 1

The correct linear inequality to represent Emma's budget for hot wings and hamburgers for her slumber party, given the costs of $0.45 per wing and $1.75 per hamburger, is 0.45x + 1.75y ≤ 90.

Step-by-step explanation:

Emma is hosting a slumber party and needs to calculate how many hot wings and hamburgers she can purchase with a budget of $90. Given that the cost of one wing is $0.45 (represented by x) and the cost of one hamburger is $1.75 (represented by y), we need to find a linear inequality that represents this scenario. The inequality that reflects the maximum amount she can spend would be 0.45x + 1.75y ≤ 90. This inequality means that the total cost of the number of wings and hamburgers must be less than or equal to $90.

Steps to Write a Linear Inequality

1. Identify the cost per item: wings are $0.45 each, and hamburgers are $1.75 each.
2. Multiply the cost per item by the quantity for each (0.45 times the number of wings plus 1.75 times the number of hamburgers).
3. Set this expression to be less than or equal to the total budget (≤ $90).

The correct linear inequality for this situation is therefore 0.45x + 1.75y ≤ 90, which translates to option a) among the choices given.