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Answer :
To solve the problem of determining how many wreaths were sold, follow these steps:
1. Define Variables:
- Let [tex]\( x \)[/tex] be the number of 18-inch wreaths sold.
- The number of 22-inch wreaths sold is six more than twice the number of 18-inch wreaths. So, we can express the number of 22-inch wreaths sold as [tex]\( 2x + 6 \)[/tex].
2. Create an Equation for Total Sales Revenue:
- Each 18-inch wreath costs [tex]$25, so the revenue from the 18-inch wreaths is \( 25x \).
- Each 22-inch wreath costs $[/tex]30, so the revenue from the 22-inch wreaths is [tex]\( 30(2x + 6) \)[/tex].
3. Set Up the Revenue Equation:
- The total revenue from selling both types of wreaths is $1030. Therefore, the equation is:
[tex]\[
25x + 30(2x + 6) = 1030
\][/tex]
4. Solve the Equation:
- Expand and simplify the equation:
[tex]\[
25x + 60x + 180 = 1030
\][/tex]
- Combine like terms:
[tex]\[
85x + 180 = 1030
\][/tex]
- Subtract 180 from both sides:
[tex]\[
85x = 850
\][/tex]
- Divide both sides by 85:
[tex]\[
x = 10
\][/tex]
- So, the number of 18-inch wreaths sold was 10.
5. Find the Number of 22-inch Wreaths Sold:
- Use the expression for the 22-inch wreaths:
[tex]\[
2x + 6 = 2(10) + 6 = 20 + 6 = 26
\][/tex]
- So, the number of 22-inch wreaths sold was 26.
In conclusion, the store sold 10 of the 18-inch wreaths and 26 of the 22-inch wreaths.
1. Define Variables:
- Let [tex]\( x \)[/tex] be the number of 18-inch wreaths sold.
- The number of 22-inch wreaths sold is six more than twice the number of 18-inch wreaths. So, we can express the number of 22-inch wreaths sold as [tex]\( 2x + 6 \)[/tex].
2. Create an Equation for Total Sales Revenue:
- Each 18-inch wreath costs [tex]$25, so the revenue from the 18-inch wreaths is \( 25x \).
- Each 22-inch wreath costs $[/tex]30, so the revenue from the 22-inch wreaths is [tex]\( 30(2x + 6) \)[/tex].
3. Set Up the Revenue Equation:
- The total revenue from selling both types of wreaths is $1030. Therefore, the equation is:
[tex]\[
25x + 30(2x + 6) = 1030
\][/tex]
4. Solve the Equation:
- Expand and simplify the equation:
[tex]\[
25x + 60x + 180 = 1030
\][/tex]
- Combine like terms:
[tex]\[
85x + 180 = 1030
\][/tex]
- Subtract 180 from both sides:
[tex]\[
85x = 850
\][/tex]
- Divide both sides by 85:
[tex]\[
x = 10
\][/tex]
- So, the number of 18-inch wreaths sold was 10.
5. Find the Number of 22-inch Wreaths Sold:
- Use the expression for the 22-inch wreaths:
[tex]\[
2x + 6 = 2(10) + 6 = 20 + 6 = 26
\][/tex]
- So, the number of 22-inch wreaths sold was 26.
In conclusion, the store sold 10 of the 18-inch wreaths and 26 of the 22-inch wreaths.
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