b. Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box. The third box contained two more pounds than the first box. The last box contained one-fourth the amount in the second box. How much candy was in each box?  

Here we have , Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box. The third box contained two more pounds than the first box. The last box contained one-fourth the amount in the second box. We need to find How much candy was in each box. Let's find out:

We have a total of 65 pounds of candy ! Let in first box we have x pounds so , second box contained twice the amount of the first box i.e.

⇒ [tex]2x[/tex]

The third box contained two more pounds than the first box i.e.

⇒ [tex]x+2[/tex]

The last box contained one-fourth the amount in the second box i.e.

⇒ [tex](\frac{1}{4})2x = \frac{x}{4}[/tex]

Therefore , Sum of pounds of candy are :

⇒ [tex]\frac{x}{2} +x+2+2x+x=65[/tex]

⇒ [tex]\frac{x}{2} +4x=63[/tex]

⇒ [tex]\frac{9x}{2}=63[/tex]

⇒ [tex]x=63(\frac{2}{9} )[/tex]

⇒ [tex]x=14[/tex]

Therefore , Candy in each box is :

First box = 14 pounds

Second box = 2x = 28 pounds

Third Box = x+2= 16 pounds

Fourth box = x/2 = 7 pounds

ibiscollingwood ibiscollingwood · Answer 2 · 2022-04-06T04:32:23+02:00

The candy in each box is shown below,

First box = 14 pounds

Second box = 2x = 2*14 = 28 pounds

Third Box = x+2=14 + 2 = 16 pounds

Fourth box = x/2 =14/2 = 7 pounds

Linear equation in one variable:

Total amount of candy is 65 pounds.

It is divided into four different boxes.

Let us consider that in first box , candy is x pounds

Since, second box contained twice the amount of the first box

So that, candy in second box = 2x

The third box contained two more pounds than the first box .

So that, candy in third box = x + 2

The last box contained one-fourth the amount in the second box .

So that, candy in last box [tex]=\frac{2x}{4}=\frac{x}{2}[/tex]

Total Sum of pounds of candy are equal to 65.

[tex]x+2x+x+2+\frac{x}{2} =65\\\\\frac{9}{2}x=63\\ \\x=63*\frac{2}{9} =14[/tex]

Hence , Candy in each box is calculated below;

First box = 14 pounds

Second box = 2x = 2*14 = 28 pounds

Third Box = x+2=14 + 2 = 16 pounds

Fourth box = x/2 =14/2 = 7 pounds

Learn more about the linear equation here:

https://brainly.com/question/14323743