Let's check each case to determine the solution to the problem.
we know that
The cost of each flower arrangements is [tex]\$28[/tex]
Statements
case A) If the price is marked down by [tex]10[/tex] percent, the new price will be [tex]\$25.20[/tex]
we know that
If the price is marked down by [tex]10[/tex] percent
then
the new price will be
[tex]10\%= \frac{10}{100} =0.10[/tex]
[tex](1-0.10)*\$28=0.90*\$28 \\= \$25.20[/tex]
[tex]\$25.20=\$25.20[/tex]
therefore
The statement case A) is True
case B) If the price is marked down by [tex]25[/tex] percent, the new price will be [tex]\$21[/tex]
we know that
If the price is marked down by [tex]25[/tex] percent
then
the new price will be
[tex]25\%= \frac{25}{100} =0.25[/tex]
[tex](1-0.25)*\$28=0.75*\$28 \\= \$21[/tex]
[tex]\$21=\$21[/tex]
therefore
The statement case B) is True
case C) If the price is marked down by [tex]50[/tex] percent, the new price will be [tex]\$19[/tex]
we know that
If the price is marked down by [tex]50[/tex] percent
then
the new price will be
[tex]50\%= \frac{50}{100} =0.50[/tex]
[tex](1-0.50)*\$28=0.50*\$28 \\= \$14[/tex]
[tex]\$14 \neq \$19[/tex]
therefore
The statement case C) is False
case D) If the price is marked down by [tex]35[/tex] percent, the new price will be [tex]\$18.20[/tex]
we know that
If the price is marked down by [tex]35[/tex] percent
then
the new price will be
[tex]35\%= \frac{35}{100} =0.35[/tex]
[tex](1-0.35)*\$28=0.65*\$28 \\= \$18.20[/tex]
[tex]\$18.20=\$18.20[/tex]
therefore
The statement case D) is True
case E) If the price is marked down by [tex]40[/tex] percent, the new price will be [tex]\$29.80[/tex]
we know that
If the price is marked down by [tex]40[/tex] percent
then
the new price will be
[tex]40\%= \frac{40}{100} =0.40[/tex]
[tex](1-0.40)*\$28=0.60*\$28 \\= \$16.80[/tex]
[tex]\$16.80 \neq \$29.80[/tex]
therefore
The statement case E) is False
