Q14. - Algebra 2

Question

FLOORING

Deion estimates that he will need between 55 and 60 ceramic tiles to retile his kitchen floor. If each tile costs $\$6.25,$ write and solve a compound inequality to determine what the cost $c$ of the tile could be.

Step-by-Step Solution

Answer

Cost of the tiles could be $343.75\le c\le 375$

Step 1 - Formula for cost of tiles

Cost $c$ of tiles is product of cost of each tile with number of tiles

Let the number of tiles be n 

As cost of one tile is $\$6.25$ so cost of required number of tiles

$\begin{array}{c}c=6.25\times n\\ c=6.25n\end{array}$

Step 2 - Inequality for number of tiles

As number of tiles between 55 and 60

So inequality for number of tiles required

$55\le n\le 60$ 

Step 3 - Inequality for cost of tiles

Using multiplication property of inequality, multiply an inequality with positive number does not reverse the sign of inequality so multiply inequality of step 2 with 6.25.

$\begin{array}{c}55\times 6.25\le n\times 6.25\le 60\times 6.25\\ 343.75\le c\le 375\end{array}$