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?

Where did the 19 come from? Also that was all just question "a" right? So confused.

To calculate how many outfits can be made, divide the total amount of material available by the amount required for each outfit:

29 1/2 yards ÷ 3/4 yard = (59/2) ÷ (3/4)

To divide fractions, you invert the divisor and multiply:

(59/2) × (4/3) = (59 × 4) ÷ (2 × 3) = 236/6

Simplifying the fraction:

236/6 = 118/3

a: Therefore, 118/3 outfits can be made.

To find out how much material will be left over, subtract the amount of material used for the outfits from the total amount available:

Total material available - (number of outfits × amount of material per outfit)

29 1/2 yards - (118/3 outfits × 3/4 yard per outfit)

To multiply mixed numbers, convert them to improper fractions:

29 1/2 = (29 × 2 + 1) / 2 = 59/2

So the equation becomes:

59/2 - (118/3 × 3/4)

To multiply fractions, multiply the numerators and denominators:

59/2 - (354/12)

To subtract fractions, we must have a common denominator:

59/2 - (354/12) = (59 × 6/2 × 6) - (354 × 2/12 × 2)

Simplifying:

(354 - 708)/12 = -354/12 = -59/2

b: Therefore, there will be -59/2 (or -29 1/2) yards of material left over. Note that this is a negative value, indicating that there is not enough material to make a whole outfit.

To find the answers to these questions, we need to perform some basic calculations.

a: To determine how many outfits can be made, we divide the total amount of material available by the amount of material required for each outfit.

Step 1: Convert the mixed number to an improper fraction.
29 1/2 can be represented as 59/2 because 29*2 + 1 = 59.

Step 2: Divide the total amount of material available by the amount of material required for each outfit.
59/2 ÷ 3/4 = 59/2 * 4/3 = 236/6 = 39 1/6

Therefore, you can make 39 complete outfits with the given material.

b: To calculate the amount of material that will be left over, we subtract the amount used for the outfits from the total amount available.

Step 1: Multiply the number of outfits by the amount of material required for each outfit.
39 * 3/4 = 29 1/4

Step 2: Subtract the above result from the total amount available.
29 1/2 - 29 1/4 = 1/4

Therefore, there will be 1/4 yard of material left over.

divide 19 1/2 by 3/4

= (39/2)(4/3) = 26

or

19.5/.75 = 26