A board that is 12 feet long must be cut into 2 pieces that have lengths in a ratio of 3 to 2. Find the lengths of the two pieces.
Let x = the longer piece.
3/5 = x/12
5x = 36
x = 7.2
12 - 7.2 = ?
variable L= length
and we have 12:2 is = 6
and then the ratio 2/3
is 2/3 L=9
check:
12-9=3 If they asking continues answer will be 3
so both sides are make sense
6=2/3(9) check from the 12 feet long we have 12= L+3= 12=12
if this helpful
6= 6
To find the lengths of the two pieces, we need to divide the 12-foot board into two pieces with lengths in a ratio of 3 to 2.
Step 1: Calculate the total ratio by adding the two parts of the ratio: 3 + 2 = 5.
Step 2: Divide the total length of the board by the total ratio to find the length of each part: 12 ft ÷ 5 = 2.4 ft.
Step 3: Multiply the length of each part by the corresponding part of the ratio.
Length of the first piece: 2.4 ft × 3 = 7.2 ft.
Length of the second piece: 2.4 ft × 2 = 4.8 ft.
Therefore, the lengths of the two pieces are 7.2 feet and 4.8 feet.
To find the lengths of the two pieces, we can set up a proportion based on the given ratio.
Let's say the lengths of the two pieces are 3x and 2x, where x is a common multiplier.
According to the given information, the total length of the board is 12 feet. So we can write the equation:
3x + 2x = 12
Simplifying the equation:
5x = 12
To find the value of x, we divide both sides of the equation by 5:
x = 12 ÷ 5
x = 2.4
Now that we have the value of x, we can find the lengths of the two pieces:
Length of the first piece = 3x = 3 * 2.4 = 7.2 feet
Length of the second piece = 2x = 2 * 2.4 = 4.8 feet
Therefore, the lengths of the two pieces are 7.2 feet and 4.8 feet.