Question

4. A music store has a 30% off all instruments sale.

a.
b.
A guitar regularly costs $45.What is the discount price? _________________________
If the regular price of an item is dollars, what is the discount price in dollars? ___________________
c.
If the sale price of a trumpet says $140. What is the regular price? _________________________

Answer 1

a. The discount price of the guitar is 31.50 (45 * 0.30).

b. If the regular price of an item is P dollars, the discount price is (0.70 * P) dollars.

c. The regular price of the trumpet is 200 (140 / 0.70).

a. The discount price of the guitar can be calculated by multiplying the regular price by the discount percentage:

Discount Price = Regular Price - (Regular Price * Discount Percentage)

In this case:

Regular Price = 45

Discount Percentage = 30%

Discount Price = 45 - 45 * 0.30

= 45 - 13.50

= 31.50

So, the discount price of the guitar is 31.50.

b.If the regular price of an item is P dollars and there is a 30% discount, the discount price (D) can be calculated using the formula:

`\[ D = P - (P * 0.30) \]`

This formula represents the original price minus 30% of the original price, which gives the discounted amount. Let's break down the steps:

1. Set up the formula:

`\[ D = P - (P * 0.30) \]`

2. Factor out P from the right side:

`\[ D = P * (1 - 0.30) \]`

3. Calculate the discount percentage:

`\[ D = P * 0.70 \]`

So, the discount price D is 70% of the regular price
`(\( P \))`. If P is the regular price, then D is the discounted price after a 30% reduction.

`if \( P = $100 \), then`

`\[ D = $100 * 0.70 = $70 \]`

Therefore, the discount price in dollars is 70% of the regular price.

c. If the sale price of a trumpet is 140, and we want to find the regular price P , we can rearrange the formula:

`\[ P = (D)/(1 - 0.30) \]`

Substitute
`\( D = $140 \)` into the formula:

`\[ P = (140)/(1 - 0.30) \]`

`\[ P = (140)/(0.70) \]`

`\[ P = 200 \]`

So, the regular price of the trumpet is $200.