Question

Select the correct answer.

Laura is planning a party for her son. She has $50 dollars remaining in her budget and wants to provide one party favor per person to at least 10 guests. She found some miniature stuffed animals for $6.00 each and some toy trucks for $4.00 each.

Which system of inequalities represents this situation, where x is the number of stuffed animals and y is the number of toy trucks?

A.
6x + 4y ≤ 50
x + y ≤ 10
B.
6x + 4y ≤ 50
x + y ≥ 10
C.
6x + 4y ≥ 50
x + y ≤ 10
D.
6x + 4y ≥ 50
x + y ≥ 10

Answer 1

Answer: B. 6x + 4y ≤ 50 x + y ≥ 10

Step-by-step explanation: To represent this situation with a system of inequalities, we need to consider two constraints: the budget and the number of guests.

The budget constraint is that the total cost of the party favors should not exceed $50. Since each stuffed animal costs $6 and each toy truck costs $4, the total cost can be expressed as 6x + 4y, where x is the number of stuffed animals and y is the number of toy trucks. To satisfy the budget constraint, we need 6x + 4y to be less than or equal to 50. This gives us the first inequality: 6x + 4y ≤ 50.

The number of guests constraint is that Laura wants to provide at least one party favor per person to at least 10 guests. This means that the total number of party favors should be greater than or equal to 10. Since each party favor is either a stuffed animal or a toy truck, the total number of party favors can be expressed as x + y, where x and y are the same as before. To satisfy the number of guests constraint, we need x + y to be greater than or equal to 10. This gives us the second inequality: x + y ≥ 10.

Therefore, the system of inequalities that represents this situation is:

6x + 4y ≤ 50 x + y ≥ 10

Hope this helps, and have a great day! =)