(a) A large consignment of components from supplier A are known to contain 4% defectives. If a batch of 8500 components is received, calculate:
(i) The proportion of defectives.
(ii) The number of defectives.
(b) Components from supplier B contain 2.5% defectives. If a batch of 12 400 components are received, calculate:
(i) The proportion of defectives.
(ii) The number of defectives.
(c) The batches of components from both suppliers are combined and sent to the production department in an assembly plant.
(i) Calculate the number of defective components in the combined batch.
(ii) Calculate the percentage of defective components in the combined batch.

### (a) Supplier A

We know that components from Supplier A contain 4% defectives, and a batch of 8500 components is received.

#### (i) Proportion of defectives
The proportion of defectives is already given as 4%, or 0.04 in decimal form.

#### (ii) Number of defectives
To calculate the number of defective components, multiply the total number of components by the proportion of defectives:
\[
\text{Number of defectives} = 0.04 \times 8500 = 340
\]

---

### (b) Supplier B

Components from Supplier B contain 2.5% defectives, and a batch of 12,400 components is received.

#### (i) Proportion of defectives
The proportion of defectives is given as 2.5%, or 0.025 in decimal form.

#### (ii) Number of defectives
To calculate the number of defective components:
\[
\text{Number of defectives} = 0.025 \times 12400 = 310
\]

---

### (c) Combined Batch

Now the batches from both Supplier A and Supplier B are combined.

#### (i) Number of defective components in the combined batch
To calculate the total number of defective components from the combined batch, add the number of defectives from both suppliers:
\[
\text{Total defective components} = 340 + 310 = 650
\]

#### (ii) Percentage of defective components in the combined batch
First, calculate the total number of components in the combined batch:
\[
\text{Total components} = 8500 + 12400 = 20,900
\]

Now, calculate the percentage of defective components:
\[
\text{Percentage of defectives} = \left(\frac{650}{20900}\right) \times 100 \approx 3.11\%
\]

---

### Summary of Results:
- **(a)(i)** Proportion of defectives for Supplier A: 0.04
- **(a)(ii)** Number of defectives for Supplier A: 340
- **(b)(i)** Proportion of defectives for Supplier B: 0.025
- **(b)(ii)** Number of defectives for Supplier B: 310
- **(c)(i)** Total number of defective components: 650
- **(c)(ii)** Percentage of defectives in the combined batch: 3.11%

---

Would you like a more detailed breakdown or further clarifications? 

Here are some related questions for further exploration:
1. What would happen if Supplier A improves its defect rate to 2%?
2. How many defectives would there be if Supplier B increases its batch size to 15,000?
3. If you rejected all defectives, what percentage of Supplier B’s components would remain?
4. How would the combined defect rate change if Supplier A sends twice as many components?
5. What is the effect on production if both suppliers reduce their defect rates by 1%?

**Tip**: When working with percentages, always convert them into decimals to make calculations easier.

A large consignment of components from supplier A are known to contain 4% defectives. If a batch of 8500 components is received, calculate: (i) The proportion of defectives. (ii) The number of defectives. Components from supplier B contain 2.5% defectives. If a batch of 12,400 components are received, calculate: (i) The proportion of defectives. (ii) The number of defectives. The batches of components from both suppliers are combined and sent to the production department in an assembly plant. (i) Calculate the number of defective components in the combined batch. (ii) Calculate the percentage of defective components in the combined batch.

Learn how to calculate the proportion and number of defective components from suppliers A and B. This problem involves percentage calculations and arithmetic to determine the number of defective components in a batch and in a combined batch. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation