Percent Increase and Decrease: Practice

Each raise multiplies by $1.10$, and the second raise is figured on the already-raised salary.

$1.10 \times 1.10 \times 40{,}000 = 1.21 \times 40{,}000 = 48{,}400$

The total rise is $21\%$, not $20\%$, because the second $10\%$ is taken of the larger amount.

The size of the change is $24{,}000 - 18{,}000 = 6{,}000$. Compare it to the original $24{,}000$.

$\frac{6{,}000}{24{,}000} \times 100\% = 0.25 \times 100\% = 25\%$

So the value dropped by $25\%$. Dividing by the new value $18{,}000$ would give the wrong $33.3\%$.

A $35\%$ discount leaves $65\%$, so $130$ is $65\%$ of the original. Divide the part by $0.65$.

$\frac{130}{0.65} = 200$

So the original price was $200$ dollars. Check: $35\%$ of $200$ is $70$ off, and $200 - 70 = 130$.

First the markup: $1.60 \times 50 = 80$ is the marked price. Then the $25\%$ discount is taken of $80$.

$0.75 \times 80 = 60$

The sale price is $60$ dollars. The $25\%$ off is figured on the marked $80$, not the original $50$ cost.

The change is $100 - 80 = 20$. Compare it to the original $80$, not the new $100$.

$\frac{20}{80} \times 100\% = 0.25 \times 100\% = 25\%$

So the price rose by $25\%$. Comparing $20$ to the new $100$ would give the wrong $20\%$.

A $12\%$ increase makes the new value $112\%$ of the original, so divide by $1.12$.

$\frac{560}{1.12} = 500$

So the original attendance was $500$. Check: $1.12 \times 500 = 560$.

First add the tax: $1.08 \times 45 = 48.60$. Then the tip is $15\%$ of that after-tax amount.

$1.15 \times 48.60 = 55.89$

The total is $55.89$ dollars. Because the tip is on the after-tax total, you cannot just add $8\%$ and $15\%$ and take $23\%$ of $45$.

The amount removed is $80 - 68 = 12$. The percent removed compares that to the original $80$.

$\frac{12}{80} \times 100\% = 0.15 \times 100\% = 15\%$

So a $15\%$ decrease takes $80$ down to $68$.

The markup amount is $52 - 40 = 12$, and a markup is measured against the cost (the original).

$\frac{12}{40} \times 100\% = 0.30 \times 100\% = 30\%$

So the markup is $30\%$. Comparing $12$ to the price $52$ would give the wrong base.

The first price is $480$. The second drop of $25\%$ leaves $75\%$ of $480$.

$0.75 \times 480 = 360$

The final price is $360$ dollars.

The size of the change is $40 - 34 = 6$. Compare it to the original $40$.

$\frac{6}{40} \times 100\% = 0.15 \times 100\% = 15\%$

So the hours dropped by $15\%$.

Test it on $100$ dollars. The raise gives $1.20 \times 100 = 120$, and the $20\%$ cut is taken of $120$.

$0.80 \times 120 = 96$

That leaves $96$ dollars, less than the $100$ you started with, so no change at all leaves more. The cut acts on the larger raised amount, so it removes more than the raise added.