Winona and Takoda are shopping for a present for their mother. The chart shows

Question

several possible presents. There is no sales tax in the state where they live.
Present Cost ($) Discount (%) Total Paid
Power tools d 15%
Water skis d + 15 25%
Jewelry d – 5 10%
a. Write two expressions in terms of d to show how much Winona and Takoda
would pay in total if they buy their mother the set of power tools...............................

Answer 1

To determine how much Winona and Takoda would pay for the set of power tools after applying the discount, we can set up the expression based on the given cost and discount percentage.

1. Cost of Power Tools (d): This is the original cost of the power tools.
2. Discount on Power Tools: The discount on the power tools is 15% of the original price \(d\).

To calculate the total paid after the discount, we first need to find out what 15% of \(d\) is:

\[ \text{Discount} = 0.15 \times d \]

Now, we subtract the discount from the original cost to find the total amount paid:

\[ \text{Total Paid} = d - \text{Discount} = d - (0.15 \times d) = d(1 - 0.15) = 0.85d \]

So, one expression to show how much they would pay for the set of power tools is:

\[ 0.85d \]

If you need a second expression using a different approach (for example, first calculating the total discount and then subtracting it), we could consider it as follows:

Find the total discount amount:

\[ \text{Total Discount} = d \times 0.15 = 0.15d \]

Then, the total paid can be written as:

\[ \text{Total Paid} = d - 0.15d = 0.85d \]

Thus, we still arrive at the same expression:

\[ 0.85d \]

In conclusion, the two expressions that represent the total paid for the set of power tools are:

1. \(0.85d\) (by subtracting the discount from the original cost),
2. \(d - 0.15d\) (which simplifies to \(0.85d\)).

Answer 2

What does the expression 0.90(d – 5) refer to? How do you know? How else
could this expression be written??????????

Answer 3

The expression \(0.90(d - 5)\) can be interpreted as follows:

• \(d\) represents the original cost of a present.
• \(- 5\) indicates a deduction of 5 dollars from the original cost \(d\), which suggests that there is some discount or markdown of $5 off the item.
• \(0.90\) signifies that after the price reduction (after subtracting 5), the customer will pay 90% of the new price.

Thus, the expression \(0.90(d - 5)\) refers to the total amount that will be paid after a $5 discount has been applied to the original cost \(d\), followed by applying a 10% discount on the new price (keeping 90% of the modified price).

Alternate Forms of the Expression

This expression can be simplified or rewritten in different ways. Here are a few methods:

1. Distributive Property: You can distribute the \(0.90\) across the terms inside the parentheses:

   \[ 0.90(d - 5) = 0.90d - 0.90 \times 5 = 0.90d - 4.5 \]

2. Factored Form: Another way to express it is to factor out the common terms, but in this case, the expression is already in a multiplied form with \(0.90\).

In summary, \(0.90(d - 5)\) represents the remaining amount to be paid after a $5 reduction followed by a 10% discount, and it can be rewritten as:

\[ 0.90d - 4.5 \]