A tea wholesaler blends together three types of tea that normally sell for and per kilogram so as to
obtain 100 kilograms of tea worth per kilogram. If the same amounts of the two higher priced teas are use
calculate how much of each type must be used in the blend.
-Workspace

Ask by Page Howell. in Australia

Jan 12,2025

Question

A tea wholesaler blends together three types of tea that normally sell for and per kilogram so as to
obtain 100 kilograms of tea worth per kilogram. If the same amounts of the two higher priced teas are use
calculate how much of each type must be used in the blend.
-Workspace

Ask by Page Howell. in Australia

Jan 12,2025

UpStudy AI · Accepted Answer

To determine how much of each type of tea must be used in the blend, let's break down the problem step-by-step.

### Given:
- **Types of Tea & Prices:**
  - Type A: \$10 per kg
  - Type B: \$11 per kg
  - Type C: \$12 per kg
- **Total Blend:**
  - **Mass:** 100 kg
  - **Value:** \$11.20 per kg

### Additional Condition:
- **Equal Amounts of Higher Priced Teas:** The amounts of Type B and Type C teas are equal.

### Let’s Define Variables:
- Let $$ x $$ = mass of Type B tea (\$11/kg)
- Let $$ x $$ = mass of Type C tea (\$12/kg) *(since amounts are equal)*
- Mass of Type A tea = $$ 100 - 2x $$ kg

### Setting Up the Equation:
The total value of the blend should equal the sum of the values of each type of tea used.

$$
(100 - 2x) \times 10 + x \times 11 + x \times 12 = 100 \times 11.20
$$

Simplifying the equation:

$$
1000 - 20x + 11x + 12x = 1120
$$

$$
1000 + 3x = 1120
$$

$$
3x = 120
$$

$$
x = 40
$$

### Calculating Each Type:
- **Type B:** $$ x = 40 $$ kg
- **Type C:** $$ x = 40 $$ kg
- **Type A:** $$ 100 - 2x = 100 - 80 = 20 $$ kg

### **Conclusion:**
To achieve the desired blend:
- **20 kg** of Type A tea (\$10/kg)
- **40 kg** of Type B tea (\$11/kg)
- **40 kg** of Type C tea (\$12/kg)

This combination will yield a 100 kg blend valued at \$11.20 per kilogram.

### **Final Answer:**
Use 20 kg of the $10 tea, and 40 kg each of the $11 and $12 teas to make the 100 kg blend.
Use 20 kg of the \$10 tea, and 40 kg each of the \$11 and \$12 teas to make the 100 kg blend.

A tea wholesaler blends together three types of tea that normally sell for and per kilogram so as to
obtain 100 kilograms of tea worth per kilogram. If the same amounts of the two higher priced teas are use
calculate how much of each type must be used in the blend.
-Workspace

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A tea wholesaler blends together three types of tea that normally sell for and per kilogram so as to obtain 100 kilograms of tea worth per kilogram. If the same amounts of the two higher priced teas are use calculate how much of each type must be used in the blend. -Workspace

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preguntas relacionadas

Latest Algebra Questions

A tea wholesaler blends together three types of tea that normally sell for and per kilogram so as to
obtain 100 kilograms of tea worth per kilogram. If the same amounts of the two higher priced teas are use
calculate how much of each type must be used in the blend.
-Workspace