Question
On a certain day a cell phone store sold iphones, Samsungs and Huaweis in the ratio \( 2: 3: 5 \). If they sold 15 Huaweis, how many cellphones did they sell altogether? ( A. 20 B. 30 C. 100 D. 150
Ask by Allan Rodriguez. in South Africa
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
They sold a total of 30 cellphones.
Solution
Let the numbers of iPhones, Samsungs, and Huaweis be in the ratio
\[
2:3:5.
\]
Let \( k \) be the common multiplier. Then the number of Huaweis is given by
\[
5k.
\]
Since 15 Huaweis were sold, we set
\[
5k = 15.
\]
Solving for \( k \):
\[
k = \frac{15}{5} = 3.
\]
The total number of cellphones sold is the sum of each type:
\[
2k + 3k + 5k = 10k.
\]
Substituting \( k = 3 \):
\[
10 \times 3 = 30.
\]
Thus, the store sold a total of \( 30 \) cellphones.
The correct answer is B. 30.
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Simplify this solution Extra Insights
If the store sold 15 Huaweis and the ratio of iPhones, Samsungs, and Huaweis is \( 2: 3: 5 \), we can let these quantities be represented by \( 2x \) (iPhones), \( 3x \) (Samsungs), and \( 5x \) (Huaweis). Since \( 5x = 15 \), we can find \( x \) by dividing: \[ x = \frac{15}{5} = 3. \] Now, we can find the number of iPhones and Samsungs sold: - iPhones: \( 2x = 2 \times 3 = 6 \) - Samsungs: \( 3x = 3 \times 3 = 9 \) Adding all of these together gives us the total number of cellphones sold: \[ 6 + 9 + 15 = 30. \] Thus, the answer is **B. 30**.
