The only items in a container a are 150 pencils and 725 pens. the ratio of the number of pencils to the number of pens in container b is 2 to 3. if all the pencils and pens in container b are placed in container a, then the ratio of the number of pencils to the number of pens in container a would be 3 to 5. what is the total number of pencils and pens in both container a and container b?
a) 5,600
b) 6,725
c) 7,125
d) 7,275
e) 8,000

Option E) 8000

Step-by-step explanation:

It is given in the question that the number of pencils and pens in a container A are 150 and 725.

Let the number of pens and pencils in container B are x and y.

As per statement " Ratio of the number of pencils to the number of pens is 2:3"

Equation will be

Or ------(1)

Second statement says "If all pens and pencils of container B are placed in container A then ratio of pencils and pens would be 3:5"

Equation will be

5(x + 150) = 3(y + 725)    [By cross multiplication]

5x + 750 = 3y + 2175

5x - 3y = 2175 - 750

5x - 3y = 1425 ------(2)

Now we put

y = 3×1425

y = 4275

Now we put y = 4275 in equation 1

x = 2850

Now (x + y) = 2850 + 4275

                  = 7125

Now Total number of pen and pencils in container A and container B

= 150 + 725 + 7125

= 8000

Therefore, Option E) is the answer

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5