Question

Yu Yan makes a wall hanging from a piece of fabric. For the first part, she cuts off of the length of the original piece of fabric. For the next two parts, she cuts off 10 inches and 5 inches from the length of the remaining fabric. In total, she cuts 35 inches from the length of the original piece of fabric. How long was the original piece of fabric? Write and solve an equation. Check your solution.​

Answer 1

Answer: Let x be the length of the original piece of fabric.

We know that:

x - y = length after first cut

(x - y) - 10 = length after second cut

((x - y) - 10) - 5 = length after third cut

Therefore, we can set up the equation:

x - y - 10 - 5 = 35

x - y = 50

To find the original length of the fabric, we can add y to both sides:

x = y + 50

The original length of the fabric is 50 inches + y inches.

We know that the total length cut was 35 inches.

So we can set up the equation:

y + 10 + 5 = 35

y = 20

So the original length of the fabric is 50 + 20 = 70 inches.

We can check the solution by using the equation:

x - y - 10 - 5 = 35

70 - 20 - 10 - 5 = 35

which is true.

Explanation: