Math Problem Statement

A purse contains ₹250 in notes of denominations ₹10 and ₹50. If the number of ₹10 notes is one more than that of ₹50 notes, find the number of notes of each denomination.

Solution

The problem you shared from the image is as follows:

Problem:
A purse contains ₹250 in notes of denominations ₹10 and ₹50. If the number of ₹10 notes is one more than that of ₹50 notes, find the number of notes of each denomination.

Solution:

Let the number of ₹50 notes be x.

  • The number of ₹10 notes is x + 1 (as given in the problem).

Now, let's form an equation based on the total amount:

  • The value of ₹50 notes = 50×x50 \times x
  • The value of ₹10 notes = 10×(x+1)10 \times (x + 1)

According to the problem, the total value of these notes is ₹250. Therefore, the equation becomes: 50x+10(x+1)=25050x + 10(x + 1) = 250

Now, solve this equation:

  1. Expand the equation: 50x+10x+10=25050x + 10x + 10 = 250

  2. Combine like terms: 60x+10=25060x + 10 = 250

  3. Subtract 10 from both sides: 60x=24060x = 240

  4. Divide by 60: x=4x = 4

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra

Formulas

Total amount equation: 50x + 10(x + 1) = 250

Theorems

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Suitable Grade Level

Grade 8-10