A 20-foot board is to be cut into two pieces whose lengths are in the...

Step 1 Given- A board of length 20 foot.
To find- The length of two pieces, if it cut into the ratio 7:3.
Step 2
Explanation- As per the question, the length of the board is 20 foot, and it cut into two pieces in the ratio of 7:3.
As the total length of the board is 20, and it must be equal to the length of the two pieces, so we have to multiply with such such number in the ratio whose sum is 20, so multiplying by 2, we get,
${\displaystyle =7\cdot 2+3\cdot 2}$
${\displaystyle =14+6}$
${\displaystyle =20}$
That is equal to the total length of the board.
So, the length of the two pieces are 14 feet and 6 feet.
Answer- Hence, the length of the two pieces are 14 feet and 6 feet.

A 20 foot board is cut into two pieces whose lengths are in the ration of 7 to 3. Find the length of the longer piece.
7 to 3 is the same as 7x to 3x where 7x is the longer piece.
Equation:
$7x+3x=20ft$
${\displaystyle 10x=20}$
${\displaystyle x=2}$
longer piece $=7x=7\cdot 2=14ft$

Step 1
Let x denote the length of one piece of the board in feet.
Since the two pieces of the board are in the ratio of 7 to 3, it follows that the other piece has a length of $\frac{7}{3}x$ in feet.
Given the total length equal to 20 feet, an equation can be set-up as shown below.
$x+\frac{7}{3}x=20$
Step 2
Multiply by 3 on both sides of the equation.
$3(x+\frac{7}{3}x)=3\times 20$
3x+7x=60
10x=60
Divide throughout by 10 to get,
$\frac{10x}{10}=\frac{60}{10}$
x=6
Step 3
If x=6, then we have
$\frac{7}{3}x=\frac{7}{3}\times 6$
=14
Therefore, the lengths of the two pieces are 6 feet and 14 feet.