Percent Problems: Additional Practice (Set 1)

Multiply by $1.20$ for the markup and $0.75$ for the sale.

$200 \times 1.20 \times 0.75 = 200 \times 0.90 = 180$

A $30\%$ discount leaves $70\%$, so $210$ is $0.70$ of the original. Divide to reverse it.

$0.70\,w = 210 \implies w = \frac{210}{0.70} = 300$

Use $I = P r t$ with $P = 2500$, $r = 0.06$, and $t = 4$.

$I = 2500 \times 0.06 \times 4 = 600$

A tip multiplies the meal by $1 + 0.15 = 1.15$, so divide the total by that factor.

$1.15\,w = 46 \implies w = \frac{46}{1.15} = 40$

The interest earned is $1240 - 1000 = 240$. From $I = P r t$, solve $r = \frac{I}{P t}$.

$r = \frac{240}{1000 \times 4} = \frac{240}{4000} = 0.06 = 6\%$

From $I = P r t$, solve for the time $t = \frac{I}{P r}$.

$t = \frac{1000}{4000 \times 0.05} = \frac{1000}{200} = 5$

The overall factor is $\frac{324}{400} = 0.81$, and it is one factor applied twice. Since $0.90 \times 0.90 = 0.81$, each factor is $0.90$.

$1 - 0.90 = 0.10 = 10\%$

So each discount was $10\%$.

The interest is $I = P r t = 250 \times 0.08 \times 3 = 60$, and the value is $P + I$.

$250 + 60 = 310$

Here $84$ is the part and the rate is $120\% = 1.20$. Solve $r\,w = p$ by dividing.

$1.20\,w = 84 \implies w = \frac{84}{1.20} = 70$

The interest is $690 - 600 = 90$. From $I = P r t$, solve $r = \frac{I}{P t}$.

$r = \frac{90}{600 \times 3} = \frac{90}{1800} = 0.05 = 5\%$

The saving is $35\%$ of the original, so it is the part with rate $0.35$. Solve for the whole.

$0.35\,w = 140 \implies w = \frac{140}{0.35} = 400$

Multiply by $1.10$ and then $1.05$.

$60000 \times 1.10 \times 1.05 = 66000 \times 1.05 = 69300$