Percent Problems: Additional Practice (Set 2)

A $20\%$ discount multiplies the original by $1 - 0.20 = 0.80$, so $48$ is $0.80$ of the original. Divide by the factor to undo it.

$0.80\,w = 48 \implies w = \frac{48}{0.80} = 60$

Adding $20\%$ of $48$ back gives $57.60$, which is wrong.

A markup multiplies the cost by $1 + 0.60 = 1.60$, so divide the price to reverse it.

$1.60\,c = 96 \implies c = \frac{96}{1.60} = 60$

Tax multiplies the pre-tax price by $1 + 0.15 = 1.15$, so divide the total by that factor.

$1.15\,w = 92 \implies w = \frac{92}{1.15} = 80$

Multiply the growth factors $1.10$ and $1.20$.

$1.10 \times 1.20 = 1.32$

That is a $32\%$ increase, not the $30\%$ from adding the rates.

Multiply the two factors, $1.20$ for the rise and $0.80$ for the fall.

$200 \times 1.20 \times 0.80 = 200 \times 0.96 = 192$

The equal rise and fall do not cancel, because the fall is taken of the larger raised price.

Multiply the two factors $0.80$ and $0.90$.

$0.80 \times 0.90 = 0.72 = 72\%$

The two discounts combine to $28\%$ off, not $30\%$.

A raise multiplies the original by $1 + 0.25 = 1.25$, so divide to reverse it.

$1.25\,w = 50000 \implies w = \frac{50000}{1.25} = 40000$

"$40\%$ larger than" is a $40\%$ increase, so multiply by $1 + 0.40 = 1.40$.

$1.40 \times 250 = 350$

Adding just $40$ would confuse "percent more than" with "percent of."

Multiply by $1.50$ for the markup and $0.60$ for the discount.

$60 \times 1.50 \times 0.60 = 60 \times 0.90 = 54$

First $60\%$ of $200$ is $0.60 \times 200 = 120$. The number times $0.80$ equals $120$, so divide.

$0.80\,n = 120 \implies n = \frac{120}{0.80} = 150$

Multiply the factors $1.20$ and $1.30$ to get the overall factor.

$1.20 \times 1.30 = 1.56$

That is a $56\%$ increase, not the $50\%$ you would get by adding the rates.

Multiply the factors $1.50$ and $0.50$.

$1.50 \times 0.50 = 0.75$

The final price is $75\%$ of the start, a $25\%$ decrease.