Susan wants to make aprons for cooking. She needs one and three fourths yards of fabric for the front of the apron and three eighths yards of fabric for the tie.
Part A: Calculate how much fabric is needed to make 3 aprons? Show every step of your work. (5 points)
Part B: If Susan originally has 7 yards of fabric, how much is left over after making the aprons? Show every step of your work. (5 points)
Part C: Does Susan have enough fabric left to make another apron? Explain why or why not. (2 points)
Part A:
To make one apron, Susan needs 1 and 3/4 yards of fabric for the front and 3/8 yards of fabric for the tie.
For three aprons, the amount of fabric needed for the front would be (1 and 3/4) x 3 = 5 and 1/4 yards.
The amount of fabric needed for the ties would be (3/8) x 3 = 9/8 yards.
So, in total, Susan would need 5 and 1/4 yards + 9/8 yards = (42/8 + 9/8) yards = 51/8 yards of fabric to make 3 aprons.
Part B:
Susan originally has 7 yards of fabric.
To make 3 aprons, Susan needs 51/8 yards of fabric.
The amount of fabric left after making the aprons would be 7 - (51/8) yards = (56/8 - 51/8) yards = 5/8 yards.
Part C:
After making the aprons, Susan has 5/8 yards of fabric left.
Since Susan would need another 51/8 yards of fabric to make another apron, she does not have enough fabric left. 5/8 yards is less than 51/8 yards. Hence, Susan does not have enough fabric left to make another apron.
Part A:
To calculate how much fabric is needed to make 3 aprons, we need to add the fabric needed for the front of the apron and the fabric needed for the tie for each apron.
Fabric needed for front of one apron = 1 and 3/4 yards
Fabric needed for tie of one apron = 3/8 yards
Fabric needed for 3 aprons = (1 and 3/4 yards) * 3 + (3/8 yards) * 3
Let's calculate each step of the work:
1 and 3/4 yards * 3 = 7/4 yards * 3 = (7 * 3)/4 = 21/4 yards
3/8 yards * 3 = 9/8 yards
Fabric needed for 3 aprons = 21/4 yards + 9/8 yards
Now let's add the fractions:
21/4 yards + 9/8 yards = (21 * 2)/4 yards + 9/8 yards = 42/4 yards + 9/8 yards = 51/8 yards
Therefore, 3 aprons would require 51/8 yards of fabric.
Part B:
To calculate how much fabric is left over after making the aprons, we need to subtract the fabric used for the aprons from the initial amount of fabric Susan has.
Initial fabric Susan has = 7 yards
Fabric used for 3 aprons = 51/8 yards
Fabric left over = 7 yards - 51/8 yards
To subtract fractions, we need a common denominator:
7 yards = 7 * 8/8 = 56/8 yards
Fabric left over = 56/8 yards - 51/8 yards = (56 - 51)/8 yards = 5/8 yards
Therefore, there would be 5/8 yards of fabric left over after making the aprons.
Part C:
To determine if Susan has enough fabric left to make another apron, we need to compare the fabric left over with the fabric needed for one apron.
Fabric left over = 5/8 yards
Fabric needed for one apron = 1 and 3/4 yards + 3/8 yards = 7/4 yards + 3/8 yards = 14/8 yards + 3/8 yards = 17/8 yards
Since the fabric needed for one apron (17/8 yards) is larger than the fabric left over (5/8 yards), Susan does not have enough fabric left to make another apron.
Part A: To calculate how much fabric is needed to make 3 aprons, we need to add the fabric needed for the front of the apron and the fabric needed for the tie.
1. Fabric needed for the front of one apron: 1 and 3/4 yards
2. Fabric needed for the tie of one apron: 3/8 yards
To find the total fabric needed for 3 aprons:
Fabric needed for the front of 3 aprons = 3 * (1 and 3/4) yards
Fabric needed for the tie of 3 aprons = 3 * (3/8) yards
Calculating the fabric needed for the front of 3 aprons:
3 * (1 and 3/4) = 3 * (7/4) = 21/4 = 5 and 1/4 yards
So, 5 and 1/4 yards of fabric is needed for the front of 3 aprons.
Calculating the fabric needed for the tie of 3 aprons:
3 * (3/8) = 9/8 = 1 and 1/8 yards
So, 1 and 1/8 yards of fabric is needed for the tie of 3 aprons.
Adding the fabric needed for the front and tie of 3 aprons:
5 and 1/4 + 1 and 1/8 = 6 and 3/8
Therefore, 6 and 3/8 yards of fabric is needed to make 3 aprons.
Part B: If Susan originally has 7 yards of fabric, we need to subtract the fabric used for making the aprons from the total amount.
Calculating the fabric used for the aprons:
Fabric used for 3 aprons = 6 and 3/8 yards
Subtracting the fabric used from the original fabric:
7 - 6 and 3/8 =
56/8 - 51/8 = 5/8
Therefore, 5/8 yards of fabric is left over after making the aprons.
Part C: To check if Susan has enough fabric left to make another apron, we need to compare the amount of fabric required for one apron with the amount of fabric left.
Fabric needed for one apron:
Fabric needed for the front = 1 and 3/4 yards
Fabric needed for the tie = 3/8 yards
Total fabric needed for one apron: 1 and 3/4 + 3/8 = 7/4 + 3/8 = 14/8 + 3/8 = 17/8 = 2 and 1/8 yards
Since Susan has 5/8 yards of fabric left, which is less than the fabric needed for one apron (2 and 1/8 yards), she does not have enough fabric left to make another apron.