The sum of two numbers is 50. The sum of ¼ of the first number and 2/3 of the other is 25. What are the numbe

Question

The sum of two numbers is 50. The sum of ¼ of the first number and 2/3 of the other is 25. What are the numbers?

Answer 1

The two numbers are a and b

a + b = 50
a/4 + 2b/3 = 25

Plug b=50 - a into the 2nd equation:

a/4 + 2(50 - a)/3 = 25 // Multiply by 4*3 = 12

3a + 8(50 - a) = 300

3a + 400 - 8a = 300

-5a + 400 = 300 // - 400

-5a = - 100 // divide by -5

a=20

Because a + b = 50:

b = 30

Answer 2

Let the first number be x, so the second is (50-x), so:

x/4 + 2(50 - x)/3 = 25.........xly thro by 12:

3x + 8(50 - x) = 300, so

3x + 400 - 8x = 300, so

400 - 5x = 300,so

5x = 100, so

x = 20, and (50-20) = 30.

So the two numbers are 20 and 30.

Always try to get the original equation in terms of one unknown rather than two. It makes the subsequent calculations a lot easier, because you only have to solve one equation, not two simultaneous ones.

Hope this helps, Twiggy.

Answer 3

equation 1. x + y = 50
equation 2. x/4 + 2y/3 = 25
From eq. 1, you get x = 50 - y, and substituting this for x in eq 2, you get the following:
50-y/4 + 2y/3 = 25 which can be written as
150-3y+8y/12 = 25
150-3y+8y = 300
5y = 150 so y = 30
Therefore x = 20

Answer 4

x = 1st number, y = 2nd number

Values of y:
y = 50 - x

1/4x + 2/3y = 25
2/3y = 25 - 1/4x
y = (25 - 1/4x) / (2/3)

Value of x:
2/3(50 - x) = 25 - 1/4x
100/3 - 2/3x = 25 - 1/4x
100/3 - 75/3 = 8/12x - 3/12x
25/3 = 5/12x
x = 20

Value of y:
= 50 - 20
= 30

Answer: 1st no. is 20, the 2nd no. is 30.

Proof (sum of 25):
= (1/4 * 20) + (2/3 * 30)
= 5 + 20
= 25

Answer 5

Let first number be X
Let second number be Y
1/4 of X+ 2/3 of Y=25
X+Y=50
so you have got 2 equations, to find X and Y solve the 2 equations simultaneously

Answer 6

x + y = 50
x/4 + 2y/3 = 25

3x + 8y = 300
- 3x - 3y = - 150----ADD
5y = 150
y = 30
x = 20