# Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. How do you find the numbers?

See full process for solving this word problem below in the Explanation section:

Let us first deal with the first sentence of this word problem.

We know from the first sentence:

We know from the second sentence:

The larger number is 12 and the smaller number is 9

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Let x be the smaller number and y be the larger number. From the given information, we have:

- 3y = 4x (Three times the larger number is equal to four times the smaller number)
- x + y = 21 (The sum of the numbers is 21)

From equation 1, we can express x in terms of y: x = (3/4)y

Substitute this expression for x into equation 2: (3/4)y + y = 21

Now solve for y: (7/4)y = 21 y = (4/7) * 21 y = 12

Substitute the value of y into equation 2 to find x: x + 12 = 21 x = 21 - 12 x = 9

So, the smaller number is 9 and the larger number is 12.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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