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

she will travel a distance in the range of 3 - 11 miles