The sum of two numbers is 105. One number is 6 times the other. Find the numbers the smaller value and the larger value.
Here's a start: 105/7 = ?
That's 15, 105/7= 15
If the larger of two numbers is divided by the smaller, the quotient is 7 and the remainder is 12. But if 3 times the greater is divided by twice the smaller, the quotient is 11 and the remainder is 12. What are the numbers?
To find the two numbers, let's proceed step by step.
Let's assume that the smaller number is x. Since the other number is 6 times the smaller number, we can say the larger number is 6x.
According to the given information, the sum of the two numbers (x and 6x) is 105. We can write this as an equation:
x + 6x = 105
Now, let's combine the like terms on the left side of the equation:
7x = 105
To isolate x, divide both sides of the equation by 7:
x = 105 / 7
Simplifying the right side:
x = 15
So, the smaller number is 15.
To find the larger number, multiply the smaller number by 6:
6x = 6 * 15
Solving the multiplication:
6x = 90
The larger number is 90.
Therefore, the smaller value is 15, and the larger value is 90.