a piece of ribbon is cut into two shorter pieces in the ratio 2.8 : 1.25

The difference in the length of the shorter pieces is 80.6 cm.

What is the length of the original piece?

Coolllllllk brooomim tryna cheat on this test thanks

reduce the ratio:

2.8 : 1.25
= 280 : 125
= 56 : 25
let the ratio of the ribbons be
56x : 25x

"The difference in the length of the shorter pieces is 80.6 cm. "

This makes no sense, I will assume you meant that the difference in the length of the two pieces is 80.6

56x - 25x = 80.6
x = 80.6/31 = 806/310 = 13/5 = 2.6

so the original piece = 56x + 25x = 81x
81x = 81(2.6) = 210.6

The original was 210.6 cm

check:
the pieces are 56(2.6) and 25(2.6) cm or
145.6 cm and 65 cm
sum = 145.6+65 = 210.6 , check!
ratio of 145.6 : 65
= 1456 : 650 ----> divide each by 520
= 2.8 : 1.25 , check!
=

210.6 yw

To find the length of the original piece of ribbon, we need to set up an equation based on the given information.

Let's assume the length of the original piece of ribbon is "x" cm.

According to the given information, the ratio of the two shorter pieces is 2.8:1.25. This means that the first shorter piece is 2.8 times larger than the second shorter piece.

Let's represent the length of the first shorter piece as 2.8y cm, and the length of the second shorter piece as 1.25y cm.

From the problem statement, we know that the difference in the length of the two shorter pieces is 80.6 cm. So we can write the equation:

2.8y - 1.25y = 80.6

Simplifying the equation:

1.55y = 80.6

To find the value of y, we divide both sides of the equation by 1.55:

y = 80.6 / 1.55

y ≈ 52

Now, we can substitute the value of y back into the expressions for the lengths of the shorter pieces:

Length of the first shorter piece = 2.8y = 2.8 * 52 cm
Length of the second shorter piece = 1.25y = 1.25 * 52 cm

Once we calculate these lengths, we can add them together to find the length of the original piece:

Length of the original piece = (2.8 * 52) + (1.25 * 52) cm

By evaluating this expression, we can determine the length of the original piece of ribbon.