Question

Basic crochet stitches are called single, double, and triple. Jada measures her average stitch size and sees that a "double crochet" stitch is not really twice as long; it uses 1/2 inch less than twice as much yarn as a single crochet stitch. Jada's "triple crochet" stitch uses 1 inch less than three times as much yarn as a single crochet stitch.

1. Write an expression that represents the amount of yarn Jada needs to crochet a scarf that includes 800 single crochet stitches, 400 double crochet stitches, and 200 triple
crochet stitches.

Answer 1

To determine the amount of yarn required for a scarf with different crochet stitches, we use the length of yarn for a single crochet stitch 's' as a base and account for the variations in double and triple crochet stitches.

Step-by-step explanation:

To find the amount of yarn Jada needs for her crochet scarf, we need to create expressions representing each stitch type based on the given information. Let's denote the length of yarn for a single crochet stitch as s.

• Single crochet stitch: uses s inches of yarn.
• Double crochet stitch: uses 2s - 1/2 inches of yarn (1/2 inch less than twice as much yarn as a single crochet).
• Triple crochet stitch: uses 3s - 1 inches of yarn (1 inch less than three times as much yarn as a single crochet).

To calculate the total amount of yarn for the scarf:

1. Calculate the total yarn used for 800 single crochet stitches: 800s
2. Calculate the total yarn used for 400 double crochet stitches: 400(2s - 1/2)
3. Calculate the total yarn used for 200 triple crochet stitches: 200(3s - 1)

Adding these together gives the expression for the total amount of yarn needed:

Total Yarn Needed = 800s + 400(2s - 1/2) + 200(3s - 1)

Answer 2

Answer: Let x be the amount of yarn needed for a single crochet stitch in inches.

Then the amount of yarn needed for a double crochet stitch is (2x - 1/2) inches.

And the amount of yarn needed for a triple crochet stitch is (3x - 1) inches.

To find the total amount of yarn needed for the scarf, we can use the following expression:

800x + 400(2x - 1/2) + 200(3x - 1)

Simplifying this expression, we get:

800x + 800x - 200 + 600x - 200

= 2000x - 400

Therefore, the expression that represents the amount of yarn Jada needs to crochet a scarf that includes 800 single crochet stitches, 400 double crochet stitches, and 200 triple crochet stitches is 2000x - 400, where x is the amount of yarn needed for a single crochet stitch in inches.

Step-by-step explanation: