To solve the problem, let's denote the two numbers by considering the given ratio. Let's say the two numbers are [tex]\(3x\)[/tex] and [tex]\(5x\)[/tex], where [tex]\(x\)[/tex] is a common multiplier. The ratio [tex]\(3:5\)[/tex] indicates that one number is [tex]\(3x\)[/tex] and the other number is [tex]\(5x\)[/tex].
We are given that one number is greater than the other by 10. Therefore, we can write the equation as:
[tex]\[ 5x - 3x = 10 \][/tex]
Simplifying this equation:
[tex]\[ 2x = 10 \][/tex]
Next, we need to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{10}{2} = 5 \][/tex]
Now, knowing the value of [tex]\(x\)[/tex], we can find the smaller number. The smaller number, according to the ratio, is [tex]\(3x\)[/tex]:
[tex]\[ 3x = 3 \times 5 = 15 \][/tex]
So, the smaller number is [tex]\(15\)[/tex].
