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Question

Difficulty: MediumLinear Equations in Two Variables

A manufacturer plans to produce two models of smartphones: Model X and Model Y. The assembly of each Model X smartphone requires 2.52.5 hours, and the assembly of each Model Y smartphone requires 44 hours. A total of 800800 hours of assembly time is allocated for producing these two models. If the manufacturer produces 120120 Model X smartphones, what is the maximum number of Model Y smartphones that can be produced using the remaining allocated assembly time?

  1. 125Answer
  2. B
    128
  3. C
    150
  4. D
    275

Answer

The maximum number of Model Y smartphones that can be produced is 125.
The correct answer is the value that satisfies the linear relation under the given constraints. Setting up the equation 2.5x+4y=8002.5x + 4y = 800 and substituting 120120 for xx results in 300+4y=800300 + 4y = 800. Subtracting 300300 from both sides yields 4y=5004y = 500, and dividing by 44 gives 125125 Model Y smartphones.

Step-by-Step Solution

1
Set up a linear equation representing the total assembly time.
2.5x+4y=8002.5x + 4y = 800, where xx is the number of Model X smartphones and yy is the number of Model Y smartphones.
The total assembly time is the sum of the time spent on Model X (2.52.5 hours per phone) and Model Y (44 hours per phone), which must equal the allocated 800800 hours.
2
Substitute the given number of Model X smartphones into the equation.
2.5(120)+4y=8002.5(120) + 4y = 800, which simplifies to 300+4y=800300 + 4y = 800.
The problem states that the manufacturer produces 120120 Model X smartphones.
3
Isolate the variable representing Model Y smartphones to find its value.
4y=5004y = 500, which simplifies to y=125y = 125.
Subtracting 300300 from both sides of the equation and then dividing by 44 isolates the variable yy.

Key Concept

Linear Equations in Two Variables
Estimated Time:1m 30s
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Topics

Linear Equations in Two Variables

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