Mary has a red ribbon and a green ribbon. The red ribbon is ycm long. The green ribbon is 15cm shorter than the red ribbon. (a) What is the length of the green ribbon? (b) What is the total length of the 2 ribbons?
The correct answer and explanation is:
Correct Answers:
(a) The length of the green ribbon is (y – 15) cm.
(b) The total length of the two ribbons is (2y – 15) cm.
300-Word Explanation:
Let us begin by analyzing the information in the problem. Mary has two ribbons. One is red and the other is green. The red ribbon is given to be y centimeters long. This means we do not have a fixed number for the red ribbon’s length, but instead a variable, y, which represents its length in centimeters.
The green ribbon is said to be 15 centimeters shorter than the red ribbon. If the red ribbon is y cm, then subtracting 15 cm from it gives the length of the green ribbon. So, the green ribbon’s length is y – 15 cm.
That answers part (a).
Next, for part (b), we are asked to find the total length of the two ribbons. This means we need to add the length of the red ribbon and the length of the green ribbon together.
- Red ribbon: y cm
- Green ribbon: y – 15 cm
Adding them:
y + (y – 15) = y + y – 15 = 2y – 15
So, the total length of the two ribbons is 2y – 15 centimeters.
This approach of using variables helps solve problems where not all quantities are known directly. The use of expressions like y – 15 and 2y – 15 is important in algebra, especially when comparing quantities or combining lengths. Understanding how to work with variables and expressions is a key part of developing good problem-solving skills in mathematics. It allows someone to represent relationships and changes clearly even when actual numbers are not yet provided.