A person has 29 1/2 yards of material available to make doll outfits. Each outfit requires 3/4 yard of material.
a: How many outfits can be made?
b: How much material will be left over?
59/2 / 3/4= 118/3= 39 1/3
so it made 39 and left 1/3
Let u = { 8,9,10,11,12,13,13}, A = {8,9,10,11}, B={8,9,12,,13}, and C = {10,12,14}.
To find out how many outfits can be made, divide the total yardage of material available by the yardage required per outfit.
a: Number of outfits = Total yardage available / Yardage required per outfit
= 29 1/2 yards / 3/4 yard
To divide by a fraction, we can multiply by its reciprocal:
= 29 1/2 yards * 4/3 yard
To simplify this fraction, we can convert 29 1/2 yards to an improper fraction:
= 59/2 yards * 4/3 yard
Now, we can multiply the numerators and denominators:
= (59 * 4) / (2 * 3) yards
= 236 / 6 yards
= 39 1/3 yards
Therefore, 39 1/3 outfits can be made.
b: To find out how much material will be left over, we can subtract the amount used for the outfits from the total yardage available.
Material left over = Total yardage available - (Number of outfits * Yardage required per outfit)
= 29 1/2 yards - (39 1/3 yards * 3/4 yard)
To subtract fractions, we need to have a common denominator:
= 29 1/2 yards - (39 1/3 yards * 9/12 yard)
Converting mixed fractions to improper fractions:
= 59/2 yards - (118/3 yards * 9/12 yard)
Now, we can multiply the numerators and denominators:
= (59 - (118 * 9/3)) / 2 yards
Simplifying the fraction:
= (59 - 354/3) / 2 yards
= (59 - 118) / 2 yards
= -59/2 yards
Therefore, there will be -59/2 yards of material left over.
To find the number of outfits that can be made, we need to divide the total amount of material available by the amount of material needed for each outfit.
a: To solve this, we can use the following equation:
Number of outfits = Total yards of material available / Yards of material needed per outfit
In this case, the person has 29 1/2 yards of material, which is equivalent to 59/2 yards. Each outfit requires 3/4 yard of material.
Number of outfits = (59/2) / (3/4)
We can simplify this by multiplying the numerator (59/2) by the reciprocal of the denominator (4/3), which is the same as multiplying by 3/4:
Number of outfits = (59/2) * (3/4)
Now, we can multiply the numerators and denominators:
Number of outfits = (59 * 3) / (2 * 4)
Number of outfits = 177/8 or 22 1/8 outfits
Therefore, the person can make 22 outfits, with 1/8 of an outfit left over.
b: To calculate the amount of material left over, we can subtract the amount of material used for the outfits from the total amount of material available.
Amount of material left over = Total yards of material available - (Number of outfits * Yards of material needed per outfit)
Using the information given, the person has 29 1/2 yards of material, which is equivalent to 59/2 yards. Each outfit requires 3/4 yard of material, and the person can make 22 outfits.
Amount of material left over = (59/2) - (22 * 3/4)
To simplify, we can multiply the denominator of the fraction part with the whole number:
Amount of material left over = (59 - (22 * 3)) / 2
Amount of material left over = (59 - 66) / 2
Amount of material left over = -7 / 2
Therefore, the answer is -3 1/2 yards. This means there isn't enough material to make a complete outfit and there's a deficit of 3 1/2 yards.