Question

A discounted concert ticket costs $\$14.50$ less than the original cost $c.$ You pay $\$57$ for the discounted ticket. The correct equation depicting this is ____, and the original cost $c$ is ___.

• A. $c+57=14.5;\$42.5$
• B. $c+14.5=57;\$42.5$
• C. $c-14.5=57;\$71.5$
• D. $c-57=14.5;\$71.5$

Answer 1

The correct option is C $c-14.5=57;\$71.5$

Detailed step-by-step solution:
The original cost of the ticket $=c$
The cost of the discounted ticket $=\$57$
As the discounted tickets cost $\$14.50$ less than the original cost, to get the expression for the cost of the discounted ticket, $\$14.50$ has to be subtracted from the original cost $c.$
I.e., cost of the discounted ticket $=c-14.50$
$\Rightarrow \$57=c-\$14.50$ (cost of the discounted ticket $=\$57)$
The equation depicting the relation between the discounted and original cost of the ticket will be:
$c-14.50=57$
Solving for the original cost, $c:$
$c-14.50=57$
$\Rightarrow c=57+14.50$
$\Rightarrow c=\$71.5$

$\Rightarrow$ Option B is correct.