Question
Jessica buys twice as many bottles of shampoo than conditioner. She paid R120 per bottle of shampoo and R150 per bottle of conditioner and a total of R2 340 . How many bottles of shampoo did she buy?
Ask by George Greene. in South Africa
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Jessica bought 12 bottles of shampoo.
Solution
Let's solve the problem step by step.
**Let:**
- \( S \) = number of shampoo bottles
- \( C \) = number of conditioner bottles
**Given:**
1. Jessica buys twice as many shampoos as conditioners:
\[
S = 2C
\]
2. Cost per shampoo bottle = R120
3. Cost per conditioner bottle = R150
4. Total amount spent = R2,340
**Set Up the Equation:**
The total cost can be expressed as:
\[
120S + 150C = 2340
\]
**Substitute \( S = 2C \) into the equation:**
\[
120(2C) + 150C = 2340
\]
\[
240C + 150C = 2340
\]
\[
390C = 2340
\]
**Solve for \( C \):**
\[
C = \frac{2340}{390} = 6
\]
**Find \( S \):**
\[
S = 2C = 2 \times 6 = 12
\]
**Answer:**
Jessica bought **12 bottles of shampoo**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
Let the number of bottles of conditioner Jessica bought be \( x \). Then, the number of shampoo bottles she bought is \( 2x \). The total cost for the shampoo is \( 120 \times 2x = 240x \), and for the conditioner, it is \( 150 \times x = 150x \). The equation based on the total amount spent becomes: \[ 240x + 150x = 2340 \] Combining like terms gives: \[ 390x = 2340 \] Now, divide both sides by 390: \[ x = \frac{2340}{390} = 6 \] So, Jessica bought 6 bottles of conditioner. Therefore, she bought: \[ 2x = 2 \times 6 = 12 \] Jessica bought 12 bottles of shampoo! Let's hear it for Jessica, the shampoo queen!
