Problem Setup: Product and Relationship of Two Numbers
Let the two positive numbers be represented by variables.
- Let the second number be $x$.
- Since the first number is five times the second number, the first number is $5x$.
Calculating the Numbers Using the Product
The problem states that the product of the two numbers is 1445.
- Equation: $(5x) \times x = 1445$
- Simplify: $5x^2 = 1445$
- Solve for $x^2$: $x^2 = \frac{1445}{5}$
- Calculate $x^2$: $x^2 = 289$
- Solve for $x$: $x = \sqrt{289}$
- Result for $x$: $x = 17$ (We take the positive root as the numbers are positive).
Now, find the values of the two numbers:
- Second number ($x$) = 17
- First number ($5x$) = $5 \times 17 = 85$
Determining the Sum of the Two Numbers
The question asks for the sum of these two numbers.
- Sum = First number + Second number
- Sum = $85 + 17$
- Sum = $102$
Therefore, the sum of the two numbers is 102.
Similar Questions
Simplify: $3((\frac{5}{3})x^2 - 28x + 15) - 5(x^2 + 6x - 15)$
- The value of $x$ satisfying the equation $x^2 + a^2 = (b - x)^2$ is:
- Out of four consecutive numbers, the sum of the first two numbers is equal to the fourth number. What is half of the sum of the four numbers?
- If $p = 5 - 2\sqrt{6}$, then find the value of $p^2 + \frac{1}{p^2}$
- Which of the following number, when added to itself 14 times gives 135 as result?
- Simplify $x(7x - 2) + 5(x^2 - 3) + 13$.
- What is the number of all positive solutions of the equation $|x \times 1| = 0$ ?
- If $a + b = 5$ and $ab = 13$, then what will be the value of $a^3 + b^3$?
- The value of $p^2 - 7p + 12$ at $p = 3$ is:
- One-sixth of a number exceeds its one-ninth by 100, the number is:
Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
