Respuesta :
Answer:
The carpenter will not be able to buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
Step-by-step explanation:
Given:
Amount a carpenter can spend at most = $250
The inequality to represent the amount he can spend on each type of board is given as:
[tex]8x+12y<250[/tex]
where [tex]x[/tex] represents '2 by 8 boards' and [tex]y[/tex] represents '4 by 4 boards'.
To determine whether the carpenter can buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
Solution :
In order to check whether the carpenter can buy 12 '2 by 8 boards' and 14 '4 by 4 boards' , we need to plugin the [tex]x=12[/tex] and [tex]y=14[/tex] in the given inequality and see if it satisfies the condition or not or in other words (12,14) must be a solution for the inequality.
Plugging in [tex]x=12[/tex] and [tex]y=14[/tex] in the given inequality
[tex]8(12)+12(14)<250[/tex]
[tex]96+168<250[/tex]
[tex]264<250[/tex]
The above statement can never be true and hence the carpenter will not be able to buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
The above statement can never be true and hence the carpenter will not be able to buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
Given that,
A carpenter has at most $250 to spend on lumber,
The inequality 8x + 12y < 250 represents,
The numbers x of 2 by 8 boards,
And the numbers y 4 by 4 boards.
We have to find,
The carpenter can buy can the carpenter buy twelve 2 by 8 boards and fourteen 4 by 4 boards.
According to the question,
The numbers x of 2 by 8 boards,
And the numbers y 4 by 4 boards.
Inequality [tex]8x + 12y < 250[/tex]
This means that a 2-by-8 board cost $8 each, while a 4-by-4 board cost $12 each.
x = 12 2-by-8 boards
y = 14 4-by-4 boards
In order to check whether the carpenter can buy 12 '2 by 8 boards' and 14 '4 by 4 boards' .
Plugin the and in the given inequality and see if it satisfies the condition or not or in other words (12,14) must be a solution for the inequality.
Putting x=12 and y=14 in the inequality,
[tex]8(12) + 12(14) <250\\96+168<250\\264<250[/tex]
Hence, The above statement can never be true and hence the carpenter will not be able to buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
For more information about Inequality click the link given below.
https://brainly.com/question/299710
