Mr. Bob wants TEN vans with a total cargo capacity of precisely 2000 ft³. He can choose from hree models with the follow capacity: small 150 ft³, medium 200 ft³, or large 250 ft³. What are Mr. Bob's purchase options?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Problem Statement:**
Mr. Bob wants TEN vans with a total cargo capacity of precisely 2000 ft³. He can choose from three models with the following capacities:
- Small: 150 ft³
- Medium: 200 ft³
- Large: 250 ft³
What are Mr. Bob’s purchase **options**?
**Analysis:**
To solve this problem, we need to determine combinations of the small, medium, and large vans that add up to exactly 2000 ft³ of cargo capacity using ten vans.
### Steps to Consider
1. **Define Variables:**
- Let \( x \) be the number of small vans.
- Let \( y \) be the number of medium vans.
- Let \( z \) be the number of large vans.
2. **Equations:**
- The total number of vans equation:
\[ x + y + z = 10 \]
- The total capacity equation:
\[ 150x + 200y + 250z = 2000 \]
3. **Solution Approach:**
- Solve the system of equations for integer values of \( x \), \( y \), and \( z \).
By examining possible integer values that satisfy both equations, determine viable combinations of vans.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fec9627-716b-4096-bc89-25e30a6ad826%2F3e14875c-7ecf-4236-87dc-6a48afb758a4%2Fhisegzg_processed.png&w=3840&q=75)
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