Math Problem Statement

3. Muthu bought x pencils at RM0.90 each and y erasers at RM1.35 each. Write an equation in terms of x and y if the total purchase costs RM40.50. 4. Write the volume, V cm³, of the cuboid in terms of x and y, where the cuboid has dimensions (3x - 2) cm, (2y + 5) cm, and 10 cm.

Solution

Let's go through each of these questions in detail.

Question 3

In question 3, Muthu buys pencils and erasers, with prices given in Malaysian Ringgit (RM). The conditions provided are:

  • Each pencil costs RM0.90.
  • Each eraser costs RM1.35.
  • Let xx be the number of pencils and yy the number of erasers.
  • The total cost is RM40.50.

We need to set up an equation for this. Since the total cost is the sum of the cost of pencils and erasers: 0.90x+1.35y=40.500.90x + 1.35y = 40.50 Converting to cents for simplicity (so the equation avoids decimals): 90x+135y=405090x + 135y = 4050

This matches option C: 2x+3y=4052x + 3y = 405 when simplified.

Question 4

This question involves finding the volume of a cuboid with given dimensions in terms of xx and yy:

  • Length: 3x23x - 2 cm
  • Width: 2y+52y + 5 cm
  • Height: 1010 cm

The volume VV of a cuboid is given by: V=length×width×heightV = \text{length} \times \text{width} \times \text{height} Substituting the dimensions: V=(3x2)(2y+5)(10)V = (3x - 2)(2y + 5)(10)

Expanding step-by-step:

  1. First, expand (3x2)(2y+5)(3x - 2)(2y + 5): (3x2)(2y+5)=6xy+15x4y10(3x - 2)(2y + 5) = 6xy + 15x - 4y - 10
  2. Now multiply this result by 10: V=10(6xy+15x4y10)=60xy+150x40y100V = 10(6xy + 15x - 4y - 10) = 60xy + 150x - 40y - 100

This matches option C: V=60xy+75x20y100V = 60xy + 75x - 20y - 100.

Let me know if you'd like further details on these solutions, or if you have any questions.

Here are five related questions to expand on these concepts:

  1. How would the equation change in question 3 if the cost per pencil were increased by RM0.10?
  2. Can we solve for specific values of xx and yy in question 3 given additional constraints?
  3. How would the volume formula change if the height of the cuboid in question 4 were a variable instead of a constant?
  4. How could we verify the units are correct in the volume formula for question 4?
  5. What other geometric properties can be calculated using the given dimensions of the cuboid?

Tip: Always convert units consistently when solving word problems, as it can simplify the math and avoid decimal errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Volume Calculation

Formulas

Total cost equation: 0.90x + 1.35y = 40.50 or 90x + 135y = 4050
Volume of a cuboid: V = length × width × height

Theorems

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Suitable Grade Level

Grade 8-10