Question

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 the carpenter can buy can the carpenter buy twelve 2 by 8 boards and fourteen 4 by 4 boards?

Answer 1

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:

$8x+12y$

where $x$ represents  '2 by 8 boards' and $y$ 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 $x=12$ and $y=14$ 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  $x=12$ and $y=14$ in the given inequality

$8(12)+12(14)$

$96+168$

$264$

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'.