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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?

Respuesta :

Answer:

Therefore total number of pencils and pens in container A is 875.

Therefore total number of pencils and pens in container B is 7125.

Step-by-step explanation:

Given that,

Container A contains 150 pencils and 725 pens.

The ratio of number of the number of pencil to the number of pen in container B is 2:3.

Let the number of pencil and number of pencil in container B be 2x and 3x respectively.

Since all pencils and pen of container B are placed in container A.

So, the number pencil and pen in container A is (150+2x) and (725+3x) respectively.

Now the ratio of pencil to pen is

[tex]=\frac{150+2x}{725+3x}[/tex]

According to the problem,

[tex]\frac{150+2x}{725+3x}=\frac 35[/tex]

[tex]\Rightarrow 5(150+2x)=3(725+3x)[/tex]

[tex]\Rightarrow 750+10x=2175+9x[/tex]

[tex]\Rightarrow 10x-9x=2175-750[/tex]

[tex]\Rightarrow x=1475[/tex]

The number pencils in container B is = 2x

                                                             =(2×1475)

                                                             =2850

The number of pens in container B is = 3x

                                                             =(3×1475)

                                                             =4425

Therefore total number of pencils and pens in container A is =(150+725)

                                                                                                          =875

Therefore total number of pencils and pens in container B is

=(2850+4425)

=7,125