Paul needs 2 1/4 yards of fabric to make a tablecloth. How many tablecloths can he make from 18 1/2 yards of fabric. Define the variable write the equation solve and label.
x = tablecloths made
18.5 = 2.25x
x = 8 and 2/9
To solve this problem, let's define the variable:
Let x represent the number of tablecloths Paul can make.
We know that Paul needs 2 1/4 yards of fabric to make one tablecloth.
Therefore, the amount of fabric needed for x tablecloths would be x times 2 1/4 yards.
The equation representing this would be:
(x) * (2 1/4) = 18 1/2
To solve the equation, we need to convert the mixed numbers to improper fractions:
(x) * (9/4) = 37/2
Next, we can simplify the equation by canceling out common factors:
(x) * (9/4) = (37/2)
Now we can solve for x by multiplying both sides of the equation by the reciprocal of 9/4, which is 4/9:
x = (37/2) * (4/9)
Multiply the numerators and denominators:
x = (37 * 4) / (2 * 9)
x = 148 / 18
Simplify the fraction:
x ≈ 8.22
Since the number of tablecloths must be a whole number, Paul can make 8 tablecloths from 18 1/2 yards of fabric
Let's define the variable 'x' as the number of tablecloths Paul can make from the given amount of fabric.
We know that Paul needs 2 1/4 yards of fabric per tablecloth. Therefore, the equation representing this relationship is:
2 1/4 * x = 18 1/2
To solve for x, we can convert the mixed numbers into improper fractions:
9/4 * x = 37/2
Now, we can simplify the equation by multiplying both sides by the reciprocal of 9/4, which is 4/9:
(9/4 * x) * (4/9) = (37/2) * (4/9)
Cancelling out common factors, the equation becomes:
x = 37/2 * 4/9
Multiplying the numerators together and the denominators together, we get:
x = (37*4) / (2*9)
x = 148 / 18
Simplifying the fraction, we have:
x = 74 / 9
Therefore, Paul can make 74/9 or approximately 8.22 tablecloths from 18 1/2 yards of fabric. However, since you can't have a fraction of a tablecloth, Paul can make 8 tablecloths from the available fabric.