Question

The dimensions and the production costs of two different solar panels are given. 50 panels of each type are ordered. Compare and determine the order of solar panels that will cost more.

Cost of 1 sq unit (Panel A) $=\$5$
Cost of 1 sq unit (Panel B) $=\$10$

Answer 1

First we find the area of panel A:
$\bullet$ Length = 29 units = 20 units + 9 units
$\bullet$ Width = 19 units = 10 units + 9 units
Let’s determine the area using the partitioning method.

$\begin{array}{ccc}& 20& 9\\ 10& 200& 90\\ 9& 180& 81\end{array}$

Area of solar panel A $=200+90+180+81=551\text{sq units.}$
Cost of 1 solar panel $=551\times \$5=\$2,755$

Let’s find the area of panel B:
$\bullet$ Length = 14 units = 10 units + 4 units
$\bullet$ Width = 35 units = 30 units + 5 units
Let’s determine the area using the partitioning method.

$\begin{array}{ccc}& 10& 4\\ 30& 300& 120\\ 5& 50& 20\end{array}$

Area of solar panel B $=300+50+120+20=490\text{sq units.}$
Cost of 1 solar panel $=490\times \$10=\$4,900$

$\$2,755<\$4,900$
As the cost of 1 solar panel A < Cost of 1 solar panel B
The cost of 50 solar panel A < Cost of 50 solar panel B
Hence, the order for solar panels B will cost more.