Question

Suzanne is shopping for items to put inside goody bags to thank her guests for attending her party. She plans to buy candy that costs $0.75 each and toys that cost $1.75 each. She must buy at least 15 toys, and she can spend no more than $40. Suzanne also wants to ensure she has more than 30 total goodies. Let c= amount of candy bought. Let t= number of toys bought. Complete the following inequalities by filling in the missing values. (2 points)
c+t>
0.75c+1.75t≤
t≥

Answer 1

To complete the inequalities based on the information provided:

1. **Total goodies**: Since Suzanne wants to ensure she has more than 30 total goodies (candy and toys), the first inequality is:
\( c + t > 30 \)

2. **Budget constraint**: She can spend no more than $40 on candy and toys. The cost of candy is $0.75 times the number of candies (c), and the cost of toys is $1.75 times the number of toys (t). Therefore, the second inequality is:
\( 0.75c + 1.75t \leq 40 \)

3. **Minimum toys**: Suzanne must buy at least 15 toys, so the third inequality is:
\( t \geq 15 \)

Putting it all together, the completed inequalities are:

1. \( c + t > 30 \)
2. \( 0.75c + 1.75t \leq 40 \)
3. \( t \geq 15 \)