Question
Terrell arranges x roses at $3.50 each with 10 carnations at $2.25 each. He makes a bouquet of flowers that averages $3.00 per flower. Select the equation that models the situation.
A.
3.50x + 2.25(10) = 3(x + 10)
B.
3.50x + 2.25 = 0.75x
C.
3.50x + 3 = 22.5(x + 10)
D.
3.50x + 2.50 = 0.75(x + 10)
A.
3.50x + 2.25(10) = 3(x + 10)
B.
3.50x + 2.25 = 0.75x
C.
3.50x + 3 = 22.5(x + 10)
D.
3.50x + 2.50 = 0.75(x + 10)
Answers
GPT-4o mini
To solve for the equation that models the situation, we need to set up the equation based on the average price of flowers.
1. The total cost of the roses is \(3.50x\).
2. The total cost of the 10 carnations is \(2.25 \times 10 = 22.50\).
3. The total number of flowers is \(x + 10\).
4. The average price per flower is given as $3.00.
We want the total cost of all flowers divided by the total number of flowers to equal the average price. Thus, we write the following equation:
\[
\frac{3.50x + 22.50}{x + 10} = 3.00
\]
Multiplying both sides by \(x + 10\) to eliminate the fraction gives us:
\[
3.50x + 22.50 = 3.00(x + 10)
\]
Expanding the right side:
\[
3.50x + 22.50 = 3.00x + 30
\]
Now, we can rearrange terms to form an equation. However, if we compare with the provided options, the original setup can already be rearranged into a simpler equation.
The correct initial form (before simplifying further) corresponds to option **A**:
\[
3.50x + 2.25(10) = 3(x + 10)
\]
Since we calculated \(2.25(10) = 22.50\), this becomes the same equation we formed:
Thus, the answer is \( \text{A. } 3.50x + 2.25(10) = 3(x + 10) \).
1. The total cost of the roses is \(3.50x\).
2. The total cost of the 10 carnations is \(2.25 \times 10 = 22.50\).
3. The total number of flowers is \(x + 10\).
4. The average price per flower is given as $3.00.
We want the total cost of all flowers divided by the total number of flowers to equal the average price. Thus, we write the following equation:
\[
\frac{3.50x + 22.50}{x + 10} = 3.00
\]
Multiplying both sides by \(x + 10\) to eliminate the fraction gives us:
\[
3.50x + 22.50 = 3.00(x + 10)
\]
Expanding the right side:
\[
3.50x + 22.50 = 3.00x + 30
\]
Now, we can rearrange terms to form an equation. However, if we compare with the provided options, the original setup can already be rearranged into a simpler equation.
The correct initial form (before simplifying further) corresponds to option **A**:
\[
3.50x + 2.25(10) = 3(x + 10)
\]
Since we calculated \(2.25(10) = 22.50\), this becomes the same equation we formed:
Thus, the answer is \( \text{A. } 3.50x + 2.25(10) = 3(x + 10) \).