Percent Increase and Decrease: Additional Practice (Set 1)

A $40\%$ discount leaves $60\%$, so multiply by $0.60$.

$0.60 \times 250 = 150$

The sale price is $150$ dollars.

A $20\%$ discount leaves $80\%$, so $36$ is $80\%$ of the original. Divide the part by $0.80$.

$\frac{36}{0.80} = 45$

So the original price was $45$ dollars. Check: $0.80 \times 45 = 36$.

The change is $345{,}000 - 300{,}000 = 45{,}000$. Compare it to the original $300{,}000$.

$\frac{45{,}000}{300{,}000} \times 100\% = 0.15 \times 100\% = 15\%$

So the value rose by $15\%$.

The size of the change is $64 - 48 = 16$. Compare it to the original $64$.

$\frac{16}{64} \times 100\% = 0.25 \times 100\% = 25\%$

So the price dropped by $25\%$. Comparing $16$ to the new $48$ would give the wrong $33.3\%$.

First the markup: $1.50 \times 30 = 45$ is the marked price. Then the $20\%$ discount is taken of $45$.

$0.80 \times 45 = 36$

The sale price is $36$ dollars. The discount is figured on the marked $45$, not the $30$ cost.

The size of the change is $75 - 66 = 9$. Compare it to the original $75$.

$\frac{9}{75} \times 100\% = 0.12 \times 100\% = 12\%$

So the average dropped by $12\%$.

First the tax: $1.06 \times 50 = 53$. Then the tip is $10\%$ of that after-tax total.

$1.10 \times 53 = 58.30$

The final amount is $58.30$ dollars. Because the tip is on the after-tax amount, you cannot simply take $16\%$ of $50$.

Apply the changes in order. The decrease gives $0.75 \times 400 = 300$, and the increase is then taken of $300$.

$1.25 \times 300 = 375$

The final value is $375$, below $400$, because the $25\%$ rise is figured on the smaller $300$.

A $45\%$ decrease leaves $55\%$, so multiply by $0.55$.

$0.55 \times 720 = 396$

So the new value is $396$.

The change is $70 - 40 = 30$. Compare it to the original $40$.

$\frac{30}{40} \times 100\% = 0.75 \times 100\% = 75\%$

So the staff grew by $75\%$. Comparing $30$ to the new $70$ would give the wrong $42.9\%$.

The first discount gives $0.70 \times 60 = 42$. The coupon then takes $10\%$ off that reduced $42$.

$0.90 \times 42 = 37.80$

The final price is $37.80$ dollars. The two cuts act on different amounts, so they do not add to $40\%$ off.

A $25\%$ increase makes the new total $125\%$ of the original, so divide by $1.25$.

$\frac{150}{1.25} = 120$

So $120$ loaves were sold before. Check: $1.25 \times 120 = 150$.