Question

Nathaniel builds birds and birdhouses using Lego blocks. Let BBB represent the number of birds and HHH represent the number of birdhouses that Nathaniel can build with his Lego blocks. 43B+215H \leq 300043B+215H≤300043, B, plus, 215, H, is less than or equal to, 3000 Nathaniel wants to build 505050 birds using Lego blocks. How many birdhouses can he build at most with the remaining Lego blocks? Choose 1 answer: Choose 1 answer: (Choice A) A Nathaniel can build at most 111 birdhouse. (Choice B) B Nathaniel can build at most 222 birdhouses. (Choice C) C Nathaniel can build at most 333 birdhouses. (Choice D) D Nathaniel can build at most 444 birdhouses.

Answer 1

Answer: 3

Step-by-step explanation:

We are given that the number of birds Nathaniel wants to build using Lego blocks is \blue{50}50start color #6495ed, 50, end color #6495ed. When we substitute \blue B = \blue {50}B=50start color #6495ed, B, end color #6495ed, equals, start color #6495ed, 50, end color #6495ed in the given inequality, we will obtain an inequality for HHH alone:

\begin{aligned}43B+215H &\leq 3000\\\\ 43(\blue {50})+215H &\leq 3000 \\\\ 215H &\leq 850\\\\ H&\leq 3 \dfrac{41}{43}\end{aligned}

43B+215H

43(50)+215H

215H

H

​

≤3000

≤3000

≤850

≤3

43

41

​

​

Hint #22 / 3

So HHH must be less than or equal to 3\dfrac{41}{43}3

43

41

​

3, start fraction, 41, divided by, 43, end fraction. However, we should remember that the number of birdhouses Nathaniel can build must be an integer.

Since 333 is the biggest integer less than or equal to 3\dfrac{41}{43}3

43

41

​

3, start fraction, 41, divided by, 43, end fraction, Nathaniel can build 333 birdhouses at most with the remaining Lego blocks.

Hint #33 / 3

Nathaniel can build at most 3 birdhouses.

Answer 2

(C) Nathaniel can build at most 3 birdhouses.

Explanation:

Given that:

`43B+215H \leq 3000`

where:

• B represents the number of birds
• H represents the number of Birdhouses

Nathaniel wants to build 50 birds(B) using lego Blocks, we want to determine how many birdhouses(H) he can build with the remaining Lego blocks.

If B=50

`43(50)+215H \leq 3000\\2150+215H \leq 3000\\\text{Subtract 2150 from both sides}\\215H \leq 3000-2150\\215H \leq 850\\\text{Divide both sides by 215}\\H \leq 3.95`

Therefore, Nathaniel can build at most 3 Birdhouses.