represent for problems a–e, translate each question into an equation.
a. what number is $\frac{4}{5}$ of 71?
b. seventy - five hundredths of 14.4 is what number?
c. what number is 50% of 150?
d. three percent of $39 is how much money?
e. what number is 25% of 64?
f. if a salesperson receives a commission of 12% of sales, what is the salesperson’s commission on $250,000 of sales?
g. find the sales tax on a $36.89 radio when the tax rate is 7 percent.
h. find the total price of the radio in problem g, including tax.
i. evaluate find the total price, including 6 percent tax, for a $6.95 dinner, a 95¢ beverage, and a $2.45 dessert.

Question

Accepted Answer

### Part a
# Explanation:
## Step1: Define variable
Let $ n $ be the number we want to find.
## Step2: Translate to equation
"Of" means multiplication, so $\frac{4}{5}$ of 71 is $ n $, so the equation is $ n=\frac{4}{5}\times71 $
# Answer:
$ n = \frac{4}{5} \times 71 $

### Part b
# Explanation:
## Step1: Define variable
Let $ n $ be the number we want to find.
## Step2: Translate to equation
"Seventy - five hundredths" is $ 0.75 $, and "of" means multiplication. So $ 0.75\times14.4=n $
# Answer:
$ n=0.75\times14.4 $

### Part c
# Explanation:
## Step1: Define variable
Let $ n $ be the number we want to find.
## Step2: Translate to equation
$ 50\%=0.5 $, and "of" means multiplication. So $ n = 0.5\times150 $
# Answer:
$ n = 0.5\times150 $

### Part d
# Explanation:
## Step1: Define variable
Let $ m $ be the amount of money we want to find.
## Step2: Translate to equation
"Three percent" is $ 0.03 $, and "of" means multiplication. So $ m=0.03\times39 $
# Answer:
$ m = 0.03\times39 $

### Part e
# Explanation:
## Step1: Define variable
Let $ n $ be the number we want to find.
## Step2: Translate to equation
$ 25\% = 0.25$, and "of" means multiplication. So $ n=0.25\times64 $
# Answer:
$ n = 0.25\times64 $

### Part f
# Explanation:
## Step1: Define variable
Let $ c $ be the commission.
## Step2: Translate to equation
The commission rate is $ 12\%=0.12 $, and the sales amount is $ \$250000 $. Commission is rate times sales, so $ c = 0.12\times250000 $
# Answer:
$ c=0.12\times250000 $

### Part g
# Explanation:
## Step1: Define variable
Let $ t $ be the sales tax.
## Step2: Translate to equation
The tax rate is $ 7\% = 0.07$, and the price of the radio is $ \$36.89 $. Tax is rate times price, so $ t=0.07\times36.89 $
# Answer:
$ t = 0.07\times36.89 $

### Part h
# Explanation:
## Step1: Recall from part g
Let $ p $ be the total price. The total price is the price of the radio plus the tax from part g. Let $ r=\$36.89 $ (radio price) and $ t $ be the tax from part g. So $ p=r + t $, and since $ t = 0.07r $, we can also write $ p=r(1 + 0.07)=1.07\times36.89 $
## Step2: Substitute values
We know $ r = 36.89 $, so $ p=1.07\times36.89 $
# Answer:
$ p = 1.07\times36.89 $

### Part i
# Explanation:
## Step1: Calculate total cost before tax
First, find the sum of the costs of dinner, beverage, and dessert. The dinner is $ \$6.95 $, beverage is $ \$0.95 $ (since $ 95$ cents $=\$0.95$), and dessert is $ \$2.45 $. So total before tax $ b=6.95 + 0.95+2.45=10.35 $
## Step2: Calculate tax
The tax rate is $ 6\%=0.06 $, so tax $ t = 0.06\times b=0.06\times10.35 $
## Step3: Calculate total price
Total price $ p=b + t=b(1 + 0.06)=1.06\times10.35 $
# Answer:
$ p = 1.06\times10.35 $

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QUESTION IMAGE

Question

Explanation:

Part a

Step1: Define variable

Step2: Translate to equation

Step1: Define variable

Step2: Translate to equation

Step1: Define variable

Step2: Translate to equation

Answer:

Part b