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Jocelyn enjoys building robots and painting pictures. It takes her a constant amount of time to build every robot, and it takes her a constant amount of time to paint every picture. She has 15 hours to build robots and paint pictures. In the following inequality, R represents the number of robots Jocelyn can build and P represents the number of paintings she can create over that time period: 2R+5P <= 15 Jocelyn wants to build 3 robots. How many paintings at most can she create in the time that remains? Choose 1 answer: (A) Jocelyn can create at most 0 paintings. (B) Jocelyn can create at most 1 painting. (C) Jocelyn can create at most 2 paintings. (D) Jocelyn can create at most 3 paintings.

Jocelyn enjoys building robots and painting pictures. It takes her a constant amount of time to build every robot, and it takes her a constant amount of time to paint every picture. She has 1515 hours to build robots and paint pictures.\newlineIn the following inequality, R R represents the number of robots Jocelyn can build and P P represents the number of paintings she can create over that time period:\newline2R+5P≤15 2 R+5 P \leq 15 \newlineJocelyn wants to build 33 robots. How many paintings at most can she create in the time that remains?\newlineChoose 11 answer:\newline(A) Jocelyn can create at most 00 paintings.\newline(B) Jocelyn can create at most 11 painting.\newline(C) Jocelyn can create at most 22 paintings.\newline(D) Jocelyn can create at most 33 paintings.

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Q. Jocelyn enjoys building robots and painting pictures. It takes her a constant amount of time to build every robot, and it takes her a constant amount of time to paint every picture. She has 1515 hours to build robots and paint pictures.\newlineIn the following inequality, R R represents the number of robots Jocelyn can build and P P represents the number of paintings she can create over that time period:\newline2R+5P≤15 2 R+5 P \leq 15 \newlineJocelyn wants to build 33 robots. How many paintings at most can she create in the time that remains?\newlineChoose 11 answer:\newline(A) Jocelyn can create at most 00 paintings.\newline(B) Jocelyn can create at most 11 painting.\newline(C) Jocelyn can create at most 22 paintings.\newline(D) Jocelyn can create at most 33 paintings.
  1. Problem and Inequality: Understand the problem and the given inequality.\newlineThe inequality 2R+5P≤152R + 5P \leq 15 represents the time constraint for building robots (RR) and painting pictures (PP). The coefficients 22 and 55 represent the constant amount of time it takes to build a robot and paint a picture, respectively. Jocelyn has a total of 1515 hours to allocate to these activities.
  2. Substitute Robots: Substitute the number of robots Jocelyn wants to build into the inequality.\newlineJocelyn wants to build 33 robots, so we replace RR with 33 in the inequality:\newline2(3)+5P≤152(3) + 5P \leq 15
  3. Time Spent on Robots: Perform the multiplication to find the time spent on building robots.\newline2(3)=62(3) = 6\newlineSo, the inequality becomes:\newline6+5P≤156 + 5P \leq 15
  4. Time Left for Painting: Subtract the time spent on building robots from the total available time to find the time left for painting.\newline15−6=915 - 6 = 9\newlineSo, the inequality now is:\newline5P≤95P \leq 9
  5. Solve for P: Divide both sides of the inequality by 55 to solve for P.\newline5P5≤95\frac{5P}{5} \leq \frac{9}{5}\newlineP≤95P \leq \frac{9}{5}\newlineP≤1.8P \leq 1.8
  6. Maximum Number of Paintings: Since Jocelyn cannot create a fraction of a painting, we round down to the nearest whole number.\newlineJocelyn can create at most 11 painting.

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