a board 28 feet long is cut into two pieces whose lengths are in the ratio 2 to 5. find the largest of the two pieces

Question

a board 28 feet long is cut into two pieces whose lengths are in the ratio 2 to 5. find the largest of the two pieces

Answer 1

The ratio is 2 to 5, or 2:5, or 2/5

The two board lengths total 28 feet, so let one be x and the other (28-x).

As a formula: 2/5 = x/(28-x)        [their ratio is 2/5]

 

Cross multiplying, 2*(28-x) = 5*x
      56 -2*x = 5*x
             56 = 7*x

               8 = x
And, the other board is (28-x), so it measures 20 ft.

Answer 2

You know that the sum of the two boards=28, so you can write an equation.

 

2(x)+5(x)=28 ft

 

x represents the number you are going to multiply the ratio by. 

 

When we simplify the equation we get 7x=28, and divide both sides by 7 to get x=4. 

 

Plug 4, back into x for the larger board and we get 5*4 which equals 20. 

Answer 3

Hi Danielle--

 

So you need 2 numbers whose ratio is 2:5, which means that one number will be 2 times "something" and the other will be 5 times that same something.

 

So, 2n + 5n = 28, so

 

7n = 28, so

 

n = 4, which means that

 

2n = 8, and 5n = 20.  The 2 boards are 8 feet and 20 feet.

 

You can check it by thinking of the 8:20 ratio as a fraction and simplifying it to its lowest terms, which would be...

 

2/5  or 2:5, so it does check out.

 

Hope this helps!

 

Matt in NY