Question

algebraic expressions
write an algebraic expression to represent each of the scenarios below. your answers must be simplified completely.
scenario\talgebraic expression
sales tax is currently 9.4 %. write an algebraic expression to represent the total amount paid for an item that costs d dollars after tax is added to the purchase.
a store is having a 30% off sale. write an algebraic expression to represent the sale price for an item that is originally priced at d dollars.
carmen receives a 5% raise every year. write an algebraic expression to represent carmen’s salary after one year if her current salary is s dollars.
let b represent the bill for dinner at your favorite restaurant. you decide to leave a 15% tip. write an algebraic expression to represent the total amount paid for dinner, including tip.
question help: video

Explanation:

Step1: Calculate total cost with sales - tax

The sales - tax rate is 9.4% or 0.094 in decimal form. The total amount paid for an item that costs D dollars is the cost of the item plus the tax. The tax amount is 0.094D. So the total amount is $D + 0.094D=(1 + 0.094)D = 1.094D$.

Step2: Calculate sale price

The store is having a 30% off sale. The discount amount is 30% or 0.3 of the original price D. So the sale price is the original price minus the discount, which is $D-0.3D=(1 - 0.3)D = 0.7D$.

Step3: Calculate salary after raise

Carmen receives a 5% or 0.05 raise every year. Her salary after one year is her current salary plus the raise amount. The raise amount is 0.05S. So her salary after one year is $S+0.05S=(1 + 0.05)S = 1.05S$.

Step4: Calculate total dinner cost with tip

The tip rate is 15% or 0.15 in decimal form. The total amount paid for dinner is the bill amount plus the tip. The tip amount is 0.15B. So the total amount is $B + 0.15B=(1+0.15)B = 1.15B$.

Answer:

1. $1.094D$
2. $0.7D$
3. $1.05S$
4. $1.15B$