Question

The product of two numbers is 152 and the sum of these two numbers is 38. What is the smaller of these two numbers?

Answer 1

factors of 152 = 2 x 2 x 2 x 19

rearrange number so we should get 38 as sum

8 + 19 = 27   8 x 19 = 152

38 + 4 = 42   38x 4 = 152

76 + 2 = 78   76 x 2 = 152

Any of these numbers will not match with your question. So something is wrong with question

Answer 2

Answer:

The smaller of these two numbers is 4.54.                  

Step-by-step explanation:

Given : The product of two numbers is 152 and the sum of these two numbers is 38.

To find : What is the smaller of these two numbers?

Solution :

Let the numbers be x and y.

The product of two numbers is 152,

i.e. $xy=152$ .....(1)

The sum of these two numbers is 38,

i.e. $x+y=38$ .......(2)

Solving (1) and (2),

Substitute x from (1) and put in (2),

$\frac{152}{y}+y=38$

$152+y^2=38y$

$y^2-38y+152=0$

$y^2-38y+152=0$

Solve by quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=1 , b=-38, c=152

$y=\frac{-(-38)\pm\sqrt{(-38)^2-4(1)(152)}}{2(1)}$

$y=\frac{38\pm\sqrt{836}}{2}$

$y=\frac{38+\sqrt{836}}{2},\frac{38-\sqrt{836}}{2}$

$y=33.45,4.54$

At y=33.45,

$x+33.45=38$

$x=38-33.45$

$x=4.55$

At y=4.54,

$x+4.54=38$

$x=38-4.54$

$x=33.46$

The two numbers are 33.45 and 4.54.

Therefore, The smaller of these two numbers is 4.54.