a 10-inch-long board is cut into two pieces that have lengths in the ratio 2:7. What is the length of each new piece?
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2:7
2+7 = 9
2/9 times 10 equals 2.22
7/9 times 10 equals 7.78
the length of first piece is 2.22 and the 2nd piece is 7.78
To find the length of each new piece, we can set up the ratio equation using the information given.
Let's represent the lengths of the two pieces as 2x and 7x, where x is a common multiplier between them.
Since the total length of the board is 10 inches, we can write the equation:
2x + 7x = 10
Combining like terms, we get:
9x = 10
To solve for x, divide both sides of the equation by 9:
x = 10/9
Now, we can substitute this value of x back into the original equation to find the lengths of the two new pieces:
Length of the first piece = 2x = 2 * (10/9) = 20/9 inches
Length of the second piece = 7x = 7 * (10/9) = 70/9 inches
Therefore, the length of the first new piece is 20/9 inches, and the length of the second new piece is 70/9 inches.