Search: ralph's clothing company has an order for 20 skirts to be made from a bolt of fabric that has 28 1/4 yd of fabric. the customer wants as many flared skirts as possible, and the rest can be straight skirts. a straight skirt uses 1 1/4 yd of fabric, and a flared skirt uses 1 1/2 yd of fabric. how many of each kind of skirt can ralph make to complete the order?
Using algebra:
Let x=number of flared skirts,
then 20-x = number of straight skirts
1.5x+1.25(20-x) ≤ 28.25
0.25x ≤ 28.25-20*1.25
x ≤ 3.25/0.25
x ≤ 13
There he can make 13 flared skirts and 7 straight skirts.
Using arithmetic:
If he made all flared skirts, he would need 20*1.5=30 yards.
For every switch he makes, he saves (1.5-1.25)=0.25 yd
Therefore he has to switch (30-28.25)/0.25=7 skirts.
He needs to make 13 flared skirts and 7 straight skirts.
To solve this problem, we need to determine how many of each type of skirt (flared and straight) Ralph's Clothing Company can make using the given amount of fabric.
Let's start by calculating the number of flared skirts that can be made. Each flared skirt uses 1 1/2 yards of fabric, and we have a total of 28 1/4 yards of fabric. To find the maximum number of flared skirts, we divide the total fabric by the fabric required for each flared skirt:
28 1/4 yards ÷ 1 1/2 yards/flared skirt = ?
To divide mixed numbers, we convert them into improper fractions. Converting 28 1/4 to an improper fraction:
28 1/4 = (4 * 28 + 1) / 4 = 113 / 4
Now we can divide:
113 / 4 ÷ 1 1/2 = (113 / 4) ÷ (3 / 2)
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction:
(113 / 4) * (2 / 3) = (113 * 2) / (4 * 3) = 226 / 12 = 18 2/12
To simplify, we can convert 2/12 to its lowest terms:
18 2/12 = 18 1/6
So, Ralph's Clothing Company can make a maximum of 18 flared skirts.
Next, we need to determine how many straight skirts can be made. Each straight skirt uses 1 1/4 yards of fabric. We already know that we have 28 1/4 yards of fabric, and we have already used part of the fabric to make the flared skirts. To find the remaining fabric, we subtract the fabric used for the flared skirts from the total fabric:
28 1/4 yards - (18 flared skirts × 1 1/2 yards/flared skirt) = ?
First, we calculate the fabric used for the flared skirts:
18 flared skirts × 1 1/2 yards/flared skirt = 27 yards
Now we subtract the fabric used for the flared skirts from the total fabric:
28 1/4 yards - 27 yards = 1 1/4 yards
We have 1 1/4 yards of fabric remaining, which is enough to make one straight skirt. Therefore, Ralph's Clothing Company can make one straight skirt.
In conclusion, Ralph's Clothing Company can make 18 flared skirts and one straight skirt to complete the order.