Question

Andre is making paper cranes decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home.

​Andre wrote the inequality 3x + 10 ≤ 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.

Answer 1

Andre can make 6 small paper cranes in 30 minutes.

Explanation:

Given data-

Time taken by Andre to build small cranes- 3minutes

Time taken to build large crane- 10 minutes

Total time allotted to him= 30 min

His preferences- Building one large crane and several small cranes.

The Inequality equation is 3​c​ + 10 ≤ 30

Since his preference is to build atleast one large crane which takes 10 minutes, he is left with 30-10 = 20 minutes to build other small cranes.

For one crane he needs, 3 minutes

Hence, he can build 6 cranes in 18 minutes. Following this, he is left with 20-18= 2 minutes. Since he needs at least 3 min to build a small crane, he cannot build a small crane in the remaining 2 min.

he builds 6 small cranes in 30 minutes

Alternatively,

3​c​ + 10 ≤ 30

Subtracting 10 from both sides

3c ≤ 20

The maximum value of c for which this equation remains valid is 6.

Thus, he builds a total of 6 cranes (small) in 30 minutes.

I hope this helps.