Answer:
At-most 3 birdhouses.
Step-by-step explanation:
Let B represent the number of birds and H represent the number of birdhouses that Nathaniel can build with his Lego blocks.
We have been given that Nathaniel builds birds and birdhouses using Lego blocks. The inequality [tex]43B+215H\leq3000[/tex] represents the number of birds and birdhouses Nathaniel could build.
To find the number of birdhouses that Nathaniel can build after making 50 birds, we will substitute B=50 in our given inequality and then solve for H.
[tex]43*50+215H\leq3000[/tex]
[tex]2150+215H\leq3000[/tex]
Let us subtract 2150 from both sides of our inequality.
[tex]2150-2150+215H\leq3000-2150[/tex]
[tex]215H\leq850[/tex]
Let us divide both both sides of our inequality by 215.
[tex]\frac{215H}{215}\leq\frac{850}{215}[/tex]
[tex]H\leq3.953488[/tex]
As Nathaniel can make build less than or equal to 3.953488 and the biggest integer less than or equal to 3.953 is 3, therefore, Nathaniel can build at-most 3 birdhouses with remaining Lego blocks.
