Question

The dimension and production costs of 2 different solar panels are given. 10 pieces of panel A and 5 pieces of panel B 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) $=\$10$

• A. Both will cost the same
• B. Panel B
• C. Panel A
• D. Cannot be determined

Answer 1

The correct option is C Panel A

First we find the area of panel A:
$\bullet$ Length $=32=30+2$
$\bullet$ Width $=15=10+5$
Let’s determine the area using the partitioning method.

$\begin{array}{ccc}& 30& 2\\ 10& 300& 20\\ 5& 150& 10\end{array}$

$\bullet$ Area of solar panel A $=300+20+150+10=480\text{sq units.}$
$\bullet$ Cost of 1 solar panel $=480\times \$5=\$2,400$
$\bullet$ Cost of 10 solar panels $=\$2,400\times 10=\$24,000$

Let’s find the area of panel B:
$\bullet$ Length = 14 units = 10 units + 4 units
$\bullet$ Width = 34 units = 30 units + 4 units

Let’s determine the area using the partitioning method.

$\begin{array}{ccc}& 10& 4\\ 30& 300& 120\\ 4& 40& 16\end{array}$

$\bullet$ Area of solar panel B $=300+40+120+16=476\text{sq units.}$
$\bullet$ Cost of 1 solar panel $=476\times \$10=\$4,760$
$\bullet$ Cost of 5 solar panels $=\$4,760\times 5=\$23,800$
$24,000>23,800$
Hence, the cost of 10 pieces of solar panel A > cost of 5 pieces of solar panel B.