carliparker13
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A business is looking to purchase two types of computers. There are 30 salespeople. Create a system of equations that models how many of each type of computer the business should buy.

1. [tex] 515x + 205y = 11,060 [/tex]
2. [tex] x + y = 30 [/tex]
3. [tex] 515x + 285y = 39 [/tex]
4. [tex] x + y = 11,000 [/tex]
5. [tex] 515x + y = 30 [/tex]
6. [tex] 20\% y = 11,000 [/tex]
7. [tex] x + 205y = 10 [/tex]
8. [tex] 515x \cdot y = 11,000 [/tex]

(Note: Equations 3 to 8 seem to have inconsistencies and might require further verification to make sense in context.)



Answer :

GinnyAnswer
Certainly! To determine how many of each type of computer the business should buy, we'll first establish a clear system of equations based on the provided data and then solve it step-by-step. Here is a refined version of the system of equations that seems to encapsulate what you want.

### Step 1: Formulate the Equations

The given problem can be modeled by a system of linear equations. From the context, it looks like we are dealing with the following:

1. An equation representing the total cost of the computers:
[tex]\[ 515x + 205y = 11060 \][/tex]

2. An equation representing the total number of computers:
[tex]\[ x + y = 30 \][/tex]

Where:
- [tex]\(x\)[/tex] is the number of computers of the first type.
- [tex]\(y\)[/tex] is the number of computers of the second type.

### Step 2: Simplify and Solve the Equations.

1. Start with the two equations:
[tex]\[ (1) \quad 515x + 205y = 11060 \][/tex]
[tex]\[ (2) \quad x + y = 30 \][/tex]

2. Solve equation (2) for [tex]\(y\)[/tex]:
[tex]\[ y = 30 - x \][/tex]

3. Substitute [tex]\(y = 30 - x\)[/tex] into equation (1):
[tex]\[ 515x + 205(30 - x) = 11060 \][/tex]

Expand and simplify:
[tex]\[ 515x + 6150 - 205x = 11060 \][/tex]

Combine like terms:
[tex]\[ 310x + 6150 = 11060 \][/tex]

Subtract 6150 from both sides:
[tex]\[ 310x = 4910 \][/tex]

4. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{4910}{310} \][/tex]
Simplify the fraction:
[tex]\[ x = \frac{4910 \div 155}{310 \div 155} \][/tex]
[tex]\[ x = \frac{491}{31} \][/tex]

5. Substitute [tex]\(x = \frac{491}{31}\)[/tex] back into [tex]\(y = 30 - x\)[/tex] to find [tex]\(y\)[/tex]:
[tex]\[ y = 30 - \frac{491}{31} \][/tex]
Convert 30 to a fraction with the same denominator (31):
[tex]\[ y = \frac{30 \times 31}{31} - \frac{491}{31} \][/tex]
[tex]\[ y = \frac{930}{31} - \frac{491}{31} \][/tex]
Subtract the fractions:
[tex]\[ y = \frac{930 - 491}{31} \][/tex]
[tex]\[ y = \frac{439}{31} \][/tex]

### Final Solution

The number of computers of the first type [tex]\(x\)[/tex] is:
[tex]\[ x = \frac{491}{31} \][/tex]

The number of computers of the second type [tex]\(y\)[/tex] is:
[tex]\[ y = \frac{439}{31} \][/tex]

Thus, the business should buy:
- [tex]\(\frac{491}{31}\)[/tex] computers of the first type,
- [tex]\(\frac{439}{31}\)[/tex] computers of the second type.

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