Question

The table shows the cost of chair "$a$" and the number of chairs "$n$"

Cost of chair "a" in shop A (in $\$$)	Number of chairs "n"
$16$	$2$
$40$	$5$
$64$	$8$

For how many chairs purchased from shop A, will the cost be the same as purchasing $16$ chairs from shop B?

• A. $10$
• B. $16$
• C. $12$
• D. $24$

Answer 1

The correct option is D $24$

For shop A:

Cost of chair "a" in shop A (in $\$$)	Number of chairs "n"	Cost per chair $\frac{a}{n}$
$16$	$2$	$\frac{16}{2}=8$
$40$	$5$	$\frac{40}{5}=8$
$64$	$8$	$\frac{64}{8}=8$

Hence the eqution is $\frac{a}{n}=8$
$a=8n$

For shop B:

Cost of chair "a" in shop A (in $\$$)	Number of chairs "n"	Cost per chair $\frac{a}{n}$
$24$	$2$	$\frac{24}{2}=12$
$60$	$5$	$\frac{60}{5}=8$
$96$	$8$	$\frac{96}{8}=8$

Hence, the equation is $\frac{b}{n}=12$,
$b=12n$

Cost of $16$ chairs in shop B:

$b=12\times 16=\$192$
Number of chairs in shop A costing $\$192$:
$a=192$
$192=8n$
$n=\frac{192}{8}=24$
$24$ chairs bought from shop A is the same as buying $16$ chairs from shop B.