Math Problem Statement

One number is 2/5 of another number the sum of the two numbers is 35. Find the two numbers use a, to separate your answers.

Solution

Let's denote the two numbers as xx and yy. According to the problem, we have the following conditions:

  1. x=25yx = \frac{2}{5}y (One number is 25\frac{2}{5} of the other)
  2. x+y=35x + y = 35 (The sum of the two numbers is 35)

We can substitute the first equation into the second equation:

25y+y=35\frac{2}{5}y + y = 35

Next, combine the terms on the left-hand side:

25y+55y=35\frac{2}{5}y + \frac{5}{5}y = 35

75y=35\frac{7}{5}y = 35

To solve for yy, multiply both sides by 57\frac{5}{7}:

y=35×57=25y = 35 \times \frac{5}{7} = 25

Now that we have yy, substitute it back into the first equation to find xx:

x=25×25=10x = \frac{2}{5} \times 25 = 10

So, the two numbers are 10 and 25.

Answer: 1010 , 2525.

Would you like more details on any part of this solution? Here are five related questions:

  1. How do you find the least common multiple (LCM) of two numbers?
  2. How would you solve if the relationship was 34\frac{3}{4} instead of 25\frac{2}{5}?
  3. How can you verify the solution by substitution?
  4. What happens if the sum of the two numbers was different, say 50?
  5. How would you solve it if the problem involved decimals instead of fractions?

Tip: When dealing with fractions, it's helpful to multiply both sides by the denominator to simplify calculations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Fractional Relationships
Linear Equations

Formulas

Fractional relation: x = (fraction) * y
Linear equation: x + y = total sum

Theorems

Basic Properties of Equations
Simplification of Fractions

Suitable Grade Level

Grades 6-8