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Nathaniel builds birds and birdhouses using Lego blocks.
Let
B represent the number of birds and
H represent the number of birdhouses that Nathaniel can build with his Lego blocks.

43 B+215 H <= 3000
Nathaniel wants to build 50 birds using Lego blocks. How many birdhouses can he build at most with the remaining Lego blocks?
Choose 1 answer:
(A) Nathaniel can build at most 1 birdhouse.
(B) Nathaniel can build at most 2 birdhouses.
(C) Nathaniel can build at most 3 birdhouses.
(D) Nathaniel can build at most 4 birdhouses.

Nathaniel builds birds and birdhouses using Lego blocks. $\newline$ Let $B$ represent the number of birds and $H$ represent the number of birdhouses that Nathaniel can build with his Lego blocks. $\newline$ $43 B+215 H \leq 3000$ $\newline$ 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.

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Modeling with linear inequalities

Full solution

Q. Nathaniel builds birds and birdhouses using Lego blocks.

\newline

Let

B

represent the number of birds and

H

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

\newline

43 B+215 H \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.

Substitute Birds in Inequality: 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 $43B + 215H \leq 3000$ . $\newline$ $43(50) + 215H \leq 3000$
Calculate Total Blocks for Birds: Calculate the total Lego blocks used for $50$ birds. $43(50) = 2150$ $2150 + 215H \leq 3000$
Subtract Blocks for Birds: Subtract the number of Lego blocks used for birds from the total available blocks to find out how many blocks are left for birdhouses. $\newline$ $3000 - 2150 = 850$ $\newline$ $215H \leq 850$
Divide by Blocks for Birdhouse: Divide both sides of the inequality by the number of Lego blocks needed for one birdhouse to find the maximum number of birdhouses Nathaniel can build. $\newline$ $215H \leq 850$ $\newline$ $H \leq \frac{850}{215}$
Solve for H: Perform the division to solve for H. $\newline$ $H \leq \frac{850}{215}$ $\newline$ $H \leq 3.953$ (approximately)
Round Down to Whole Number: Since Nathaniel cannot build a fraction of a birdhouse, we round down to the nearest whole number. $H \leq 3$
Choose Correct Answer: Choose the correct answer from the given options. $\newline$ Nathaniel can build at most $3$ birdhouses.

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