Susan uses 15 rolls of ribbon to decorate 10 wedding baskets. Each roll of ribbon is 5 3/8 yards long. After she decorates the baskets, she decides to cut off another 3/4 yard from the ribbon of each basket. Write and simplify an expression to fin out how much ribbon was used on the baskets.
Please show work.
L = 15x + 15y
L = 15(x + y)
x = 5 3/8 Yards
y = 3/4 Yard
L = Total length
x + y = 5 3/8 + 3/4 = 43/8 + 6/8 = 49/8 = 6 1/8 Yards.
L=15 * 49/8 = 91.875 Yards = 91 7/8 Yds.
To find out how much ribbon was used on the baskets, we need to calculate the total length of ribbon used before and after cutting off 3/4 yard from each basket.
First, let's find the total length of ribbon used before cutting. We know that Susan uses 15 rolls of ribbon, and each roll is 5 3/8 yards long. To calculate the total length of ribbon used before cutting, we multiply the number of rolls by the length of each roll:
Total length before cutting = 15 rolls * 5 3/8 yards/roll
To simplify the calculation, let's convert the mixed number 5 3/8 to an improper fraction. To do this, we multiply the whole number (5) by the denominator (8) and add the numerator (3) to get the new numerator. The denominator remains the same:
5(8) + 3 = 40 + 3 = 43
So, 5 3/8 is equal to 43/8.
Now, we can substitute into the equation:
Total length before cutting = 15 rolls * 43/8 yards/roll
To multiply fractions, we multiply the numerators (15 * 43) and the denominators (8):
Total length before cutting = (15 * 43)/(8) yards
To simplify this expression, we can multiply the numerator (15 * 43) to get the product and keep the denominator (8) the same:
Total length before cutting = 645/8 yards
Now, let's find the total length of ribbon used after cutting off 3/4 yard from each basket. Since she has 10 baskets and cuts off 3/4 yard from each, we need to subtract 3/4 from the total length before cutting:
Total length after cutting = Total length before cutting - 10 baskets * 3/4 yards/basket
To subtract fractions, we require a common denominator. The denominator of the first fraction is 8, which is also the denominator of the second fraction. So, we can subtract the numerators directly:
Total length after cutting = 645/8 - 10 * 3/4
To multiply 10 by 3/4, we multiply the numerators (10 * 3) and the denominators (1 * 4):
Total length after cutting = 645/8 - 30/4
To add or subtract fractions, they must have the same denominator. So we need to convert 30/4 to have a denominator of 8:
30/4 = 30/4 * 2/2 = 60/8
Now we can substitute the values into the equation:
Total length after cutting = 645/8 - 60/8
To subtract the fractions, we subtract the numerators and keep the denominator the same:
Total length after cutting = (645 - 60)/8 yards
Total length after cutting = 585/8 yards
Therefore, the expression to find out how much ribbon was used on the baskets is (645/8) - (585/8) yards.
Mrs. Layla bought 12 rolls of pink ribbon and some rolls of yellow ribbon. The total cost of the rolls of ribbon is $45. Each roll costs $3. How many rolls of yellow ribbon did Mrs. Layla buy?
please show work