Nathaniel builds birds and birdhouses using Lego blocks. $\newline$ Let $B$ represent the number of birds and $\newline$ $H$ represent the number of birdhouses that Nathaniel can build with his Lego blocks. $\newline$ $43B + 215H \leq 3000$ $\newline$ Nathaniel wants to build $50$ birds using Lego blocks. How many birdhouses can he build at most with the remaining Lego blocks? $\newline$ Choose $1$ answer: $\newline$ (A) Nathaniel can build at most $1$ birdhouse. $\newline$ (B) Nathaniel can build at most $2$ birdhouses. $\newline$ (C) Nathaniel can build at most $3$ birdhouses. $\newline$ (D) Nathaniel can build at most $4$ birdhouses.

Full solution

Q. Nathaniel builds birds and birdhouses using Lego blocks.

\newline

Let

B

represent the number of birds and

\newline

H

represent the number of birdhouses that Nathaniel can build with his Lego blocks.

\newline

43B + 215H \leq 3000

\newline

Nathaniel wants to build

50

birds using Lego blocks. How many birdhouses can he build at most with the remaining Lego blocks?

\newline

Choose

1

answer:

\newline

(A) Nathaniel can build at most

1

birdhouse.

\newline

(B) Nathaniel can build at most

2

birdhouses.

\newline

3

birdhouses.

\newline

(D) Nathaniel can build at most

4

birdhouses.

Understand the inequality: Understand the given inequality and what it represents. $\newline$ The inequality $43B + 215H \leq 3000$ tells us that the total number of Lego blocks used to build birds ( $B$ ) and birdhouses ( $H$ ) cannot exceed $3000$ . Each bird requires $43$ blocks, and each birdhouse requires $215$ blocks.
Substitute number of birds: Substitute the number of birds Nathaniel wants to build into the inequality. $\newline$ Nathaniel wants to build $50$ birds, so we substitute $B$ with $50$ in the inequality: $\newline$ $43(50) + 215H \leq 3000$
Calculate blocks for birds: Calculate the number of Lego blocks used for $50$ birds. $\newline$ $43(50) = 2150$ $\newline$ So, Nathaniel will use $2150$ blocks for the birds.
Subtract blocks for birds: Subtract the number of blocks used for birds from the total limit to find out how many blocks are left for birdhouses. $\newline$ $3000 - 2150 = 850$ $\newline$ Nathaniel has $850$ blocks left for building birdhouses.
Divide remaining blocks for birdhouses: Divide the remaining number of blocks by the number of blocks required for one birdhouse to find out the maximum number of birdhouses Nathaniel can build. $\newline$ $850 \div 215 = 3.95348837$ $\newline$ Since Nathaniel cannot build a fraction of a birdhouse, he can build at most $3$ birdhouses.