Question

What is the answer in this question ? Macy is painting a design that contains two repeating patterns.One pattern repeats every 8 inches.The other repeats every 12 inches.The design is 19 feet long .Both pattern begin at the same place. Use the pattern pieces to create a sample to determine the number of times the patterns begins in the samen place.

Answer 1

The correct answer is:

10 times.

Step-by-step explanation:

We first find the LCM, or least common mulitple, of 8 and 12. To do this, we find the prime factorization of each:

8 = 2*4

4 = 2*2

8 = 2*2*2

12 = 4*3

4 = 2*2

12 = 2*2*3

To find the LCM, we take the common factors and multiply by the uncommon ones. The common factors are 2*2; the uncommon are 2 and 3:

2*2*2*3 = 24

The LCM is 24. This means that every 24 inches, both patterns will repeat.

The patterns are both at the beginning of the design. Then every 24 inches, or 2 feet, both patterns repeat.

19/2 = 9.5

There are an additional 9 times that the patterns repeat; this is 1+9 = 10 total times.

Answer 2

19 feet = 19 × 12 = 228 inches.

0
12
24
36
48
60
72
84
96
108
120
132
144
156
168
180
192
204
216
228

The answer is 10