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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.
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.
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