Percent Problems: Practice

A discount multiplies by $1 - r$, and you keep $100\% - 20\% = 80\%$, so the factor is $0.80$.

$0.80 \times 50 = 40$

Sales tax is an increase, so the factor is $1 + 0.05 = 1.05$.

$1.05 \times 60 = 63$

Percent change compares the change to the original. The change is $50 - 40 = 10$, and the original is $40$.

$\frac{10}{40} = 0.25 = 25\%$

Dividing by the new value $50$ would wrongly give $20\%$.

The drop is $500 - 400 = 100$, measured against the original $500$.

$\frac{100}{500} = 0.20 = 20\%$

A markup is an increase on the cost, so multiply by $1 + 0.40 = 1.40$.

$1.40 \times 30 = 42$

A commission is the part $r \cdot (\text{sales})$ with $r = 0.06$.

$0.06 \times 2500 = 150$

Multiply by the increase factor $1 + 0.08 = 1.08$.

$1.08 \times 25 = 27$

A $25\%$ discount leaves $75\%$, so multiply by $0.75$.

$0.75 \times 120 = 90$

The drop is $240 - 180 = 60$, measured against the original $240$.

$\frac{60}{240} = 0.25 = 25\%$

A markup multiplies the cost by $1 + 0.30 = 1.30$.

$1.30 \times 50 = 65$

The commission is $r \cdot (\text{sales})$ with $r = 0.03$.

$0.03 \times 90000 = 2700$

A $30\%$ discount leaves $70\%$, so multiply by $0.70$.

$0.70 \times 90 = 63$