The sum of two numbers is 31. 2/3 of one of the numbers is equal to 5/8 of the other. Find the two numbers.

Answer 1

Let's call the two numbers x and y. We know that:

x + y = 31 (the sum of the two numbers is 31)

We also know that:

(2/3)x = (5/8)y

To solve this problem, we need to use algebra to find the values of x and y that satisfy both equations. Here's how we can do that:

First, we can simplify the second equation by multiplying both sides by the least common multiple of the denominators of the fractions (which is 24):

24(2/3)x = 24(5/8)y

Simplifying, we get:

16x = 15y

Now we have two equations:

x + y = 31

16x = 15y

We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to get an equation with just one variable. Let's solve for x in terms of y:

x = (15/16)y

Substituting this into the first equation, we get:

(15/16)y + y = 31

Simplifying:

(31/16)y = 31

y = 16

Now we can find x by substituting y = 16 into either equation:

x + 16 = 31

x = 15

So the two numbers are 15 and 16.

Answer 2

Find the number such that when 3/4 of it is added to 3 1/3, the sum is the same as when 2/3 if it is subtracted from 6 1/2

Answer 3

Let's call the number we're trying to find "x".

We can write the first part of the problem as an equation:

3/4 x + 3 1/3 = ...

And we can write the second part of the problem as an equation:

6 1/2 - 2/3 x = ...

We want both equations to have the same answer, so we can set them equal to each other:

3/4 x + 3 1/3 = 6 1/2 - 2/3 x

Now we can solve for x. First, let's simplify the expressions on the right side of the equation:

3/4 x + 10/3 = 13/2 - 2/3 x

Next, we'll move all the x terms to one side and all the constant terms to the other side:

3/4 x + 2/3 x = 13/2 - 10/3

Multiplying both sides by the least common multiple of 4 and 3 (which is 12) to eliminate fractions, we get:

9x + 8x = 78 - 40

17x = 38

x = 38/17

So the number we're looking for is 38/17 (or approximately 2.235).

Answer 4

Find the number such that when 3/4 of it is added to 3 1/2, the sum is the same as when 2/3 if it is subtracted from 6 1/2

Answer 5

Let's call the number we're trying to find "x".

We can write the first part of the problem as an equation:

3/4 x + 3 1/2 = ...

And we can write the second part of the problem as an equation:

6 1/2 - 2/3 x = ...

We want both equations to have the same answer, so we can set them equal to each other:

3/4 x + 3 1/2 = 6 1/2 - 2/3 x

Now we can solve for x. First, let's simplify the expressions on the right side of the equation:

3/4 x + 7/2 = 13/2 - 2/3 x

Next, we'll move all the x terms to one side and all the constant terms to the other side:

3/4 x + 2/3 x = 13/2 - 7/2

Multiplying both sides by the least common multiple of 4 and 3 (which is 12) to eliminate fractions, we get:

9x + 8x = 24 - 42

17x = -18

x = -18/17

So the number we're looking for is -18/17 (or approximately -1.059).