Aiman had a roll of wire. He made 35 stars and 20 triangles in a day. The length of wire he used for 5 triangles is the same as 4 stars. In the morning, he used 12.48 m of wire to make 4/7 of the stars and 7/10 of the triangles. He made the remaining stars and triangles in the afternoon.
(a) How many triangles can be made using the same length of wire used in the morning?
(b) What was the length of wire he used to make the remaining stars in the afternoon?
To answer these questions, we need to gather the relevant information given in the problem and calculate accordingly.
Let's start by calculating the length of wire used for 1 triangle and 1 star.
Given:
- For 5 triangles, the length of wire used is the same as 4 stars.
We can set up a proportion to find the length of wire used for 1 triangle and 1 star:
5 triangles = 4 stars
1 triangle = 4/5 stars
Now, we know that in the morning, Aiman used 12.48 m of wire to make 4/7 of the stars and 7/10 of the triangles.
Let's calculate the length of wire used for 1 star and 1 triangle in the morning:
Stars used in the morning = (4/7) * total stars
Triangles used in the morning = (7/10) * total triangles
Given:
Stars used in the morning = 4/7
Triangles used in the morning = 7/10
Total stars = 35
Total triangles = 20
Stars used in the morning = (4/7) * 35 = 20
Triangles used in the morning = (7/10) * 20 = 14
Now, we can calculate the length of wire used for 1 star and 1 triangle in the morning:
Length of wire used for 1 star in the morning = 12.48 m / 20 stars
Length of wire used for 1 triangle in the morning = 12.48 m / 14 triangles
Next, we need to calculate the lengths of wire needed for one triangle and one star based on the information given. Let's call these lengths "T" (length of wire for 1 triangle) and "S" (length of wire for 1 star).
Since the length of wire used for 5 triangles is the same as 4 stars, we can set up a proportion:
5T = 4S
Now, we can solve for T:
T = (4/5) * S
We also know that the length of wire used for 1 star in the morning is 12.48 m / 20 stars, so we can set up another equation:
S = 12.48 m / 20 stars
Now, we can calculate the length of wire used for 1 triangle in the morning:
T = (4/5) * (12.48 m / 20 stars)
T = (4/5) * 12.48 m / 20
To answer part (a), we need to calculate how many triangles can be made using the same length of wire used in the morning, which is T.
Finally, to answer part (b), we need to calculate the length of wire used to make the remaining stars in the afternoon. We know that Aiman made the remaining stars in the afternoon, so the length of wire used for the remaining stars would be the total length of wire used for stars minus the length used in the morning.
I hope this explanation helps you understand the steps to solve this problem!