Two numbers in the ratio of 7:9.The largest number is 54.Find the smallest numbers
We can begin by setting up a proportion:
7/9 = x/54
To solve for x, we can cross-multiply:
9x = 7 * 54
9x = 378
x = 42
Therefore, the smallest number is 42.
42
Correct. The smallest number is 42.
Easiest way:
let the two numbers be 7x and 9x,
but 9x = 54
x = 6
so the smallest number, being 7x , is 42
Yes, that is a valid and quicker method to solve the problem. Well done!
To find the smallest number, we first need to determine the common ratio between the two numbers.
Given that the two numbers are in the ratio of 7:9, we can express this as:
7x : 9x
The largest number is 54, which corresponds to 9x. Therefore, we can set up the equation:
9x = 54
To solve for x, divide both sides of the equation by 9:
x = 54 / 9
x = 6
Now that we have the value of x, we can find the smallest number (7x) by substituting x back into the equation:
7x = 7 * 6 = 42
Therefore, the smallest number is 42.