1. dana buys dress shirts from a clothing manufacturer for s dollars each, and then sells the dress shirts…
1. dana buys dress shirts from a clothing manufacturer for s dollars each, and then sells the dress shirts in her retail clothing store at a 35% markup. (example 1)\na. write the markup as a decimal. \nb. write an expression for the retail price of the dress shirt. \nc. what is the retail price of a dress shirt that dana purchased for $32.00? \nd. how much was added to the original price of the dress shirt? \nlist the markup and retail price of each item. round to two decimal places when necessary. (example 1)\nitem price markup % markup retail price\n2. hat $18 15%\n3. book $22.50 42%\n4. shirt $33.75 75%
Answer
Explanation:
Step1: Convert percentage to decimal
To convert a percentage to a decimal, divide by 100. So for 35%, the decimal - form is $35\div100 = 0.35$.
Step2: Find retail - price expression
The retail price $r$ of an item that costs $s$ dollars with a 35% markup is the cost plus the markup amount. The markup amount is 35% of $s$, or $0.35s$. So the expression for the retail price is $r=s + 0.35s=1.35s$.
Step3: Calculate retail price for $s = 32$
If $s = 32$, then the retail price $r=1.35\times32=43.2$.
Step4: Calculate markup amount for $s = 32$
The markup amount $m$ is 35% of 32. So $m = 0.35\times32 = 11.2$.
Step5: Calculate markup and retail price for hat
For the hat with a price of $18$ and a 15% markup:
- Markup as a decimal: $15\div100 = 0.15$.
- Markup amount: $m=0.15\times18 = 2.70$.
- Retail price: $r=18 + 2.70=20.70$.
Step6: Calculate markup and retail price for book
For the book with a price of $22.50$ and a 42% markup:
- Markup as a decimal: $42\div100 = 0.42$.
- Markup amount: $m = 0.42\times22.50=9.45$.
- Retail price: $r=22.50+9.45 = 31.95$.
Step7: Calculate markup and retail price for shirt
For the shirt with a price of $33.75$ and a 75% markup:
- Markup as a decimal: $75\div100 = 0.75$.
- Markup amount: $m=0.75\times33.75 = 25.3125\approx25.31$.
- Retail price: $r=33.75+25.31=59.06$.
Answer:
a. $0.35$ b. $1.35s$ c. $$43.20$ d. $$11.20$
| Item | Price | Markup % | Markup | Retail Price |
|---|---|---|---|---|
| Hat | $$18$ | $15%$ | $$2.70$ | $$20.70$ |
| Book | $$22.50$ | $42%$ | $$9.45$ | $$31.95$ |
| Shirt | $$33.75$ | $75%$ | $$25.31$ | $$59.06$ |