College

A store sells gift cards in preset amounts. You can purchase gift cards for [tex]\$10[/tex] or [tex]\$15[/tex]. You have spent [tex]\$220[/tex] on combinations of gift cards.

Let [tex]x[/tex] be the number of gift cards for [tex]\$10[/tex], and let [tex]y[/tex] be the number of gift cards for [tex]\$15[/tex]. Write an equation in standard form that represents this situation.

A. [tex]10y + 15x = 220[/tex]

B. [tex]10x - 220 = 15y[/tex]

C. [tex]10y - 15x = 220[/tex]

D. [tex]10x + 15y = 220[/tex]

Answer :

To solve this problem, we need to form an equation that reflects the situation described:

1. Understand the Variables:
- Let [tex]\( x \)[/tex] be the number of gift cards costing [tex]$10 each.
- Let \( y \) be the number of gift cards costing $[/tex]15 each.

2. Form the Equation:
- You want the total cost of the gift cards to equal [tex]$220.
- Therefore, the equation should represent the total amount spent as the sum of both $[/tex]10 and [tex]$15 gift cards.

3. Write the Equation:
- For each $[/tex]10 gift card, you spend [tex]$10, so the total spent on these is \( 10x \).
- For each $[/tex]15 gift card, you spend [tex]$15, so the total spent on these is \( 15y \).
- Therefore, the equation combining both types of cards to reach a total of $[/tex]220 is:
[tex]\[
10x + 15y = 220
\][/tex]

4. Verification with Options:
- Compare with provided options:

A. [tex]\( 10y + 15x = 220 \)[/tex] (Incorrect order of coefficients)

B. [tex]\( 10x - 220 = 15y \)[/tex] (Incorrect formulation)

C. [tex]\( 10y - 15x = 220 \)[/tex] (Incorrect order and operation)

D. [tex]\( 10x + 15y = 220 \)[/tex] (Correct equation)

The correct equation that fits the situation, [tex]\( 10x + 15y = 220 \)[/tex], is option D.

Other Questions