Fresh Market is making 22 1/2 pounds of trail mix. 1/3 of the mix will be raisins, 1/5 of the mix will be M&M’s candy, and the remainder of the mix will be nuts. How many pounds of nuts are needed for the trail mix? Express the answer as a fraction in simplest form. (1 point)
pounds
To find the number of pounds of nuts needed for the trail mix, first find the total proportion of the mix that is not raisins or M&M's candy by adding the proportions that are: 1/3 + 1/5 = 5/15 + 3/15 = 8/15
Then subtract this proportion from 1 to find the proportion of the mix that is nuts: 1 - 8/15 = 7/15.
Finally, multiply this proportion by the total weight of the trail mix to find the weight of the nuts: 7/15 * 22 1/2 = (7/15) * (45/2) = (7*45) / (15*2) = 315/30 = 315/30 = 63/6 = 10 1/2 pounds. Answer: \boxed{10\frac{1}{2}}\text{ pounds}.
In a 90-minute time period, Gina watched TV, texted a friend, and read a book. She spent 3/5 of the time watching TV and 1/6 of the remainder of the time texting a friend. How much time did Gina spend reading?
To find the amount of time Gina spent reading, we first need to find the amount of time she spent watching TV and texting combined.
Gina spent 3/5 of the 90-minute time period watching TV, which is (3/5) * 90 = 54 minutes.
This means she has 90 - 54 = 36 minutes left for texting and reading.
Gina spent 1/6 of the remaining 36 minutes texting, which is (1/6) * 36 = 6 minutes.
Therefore, Gina spent 36 - 6 = 30 minutes reading.
Answer: Gina spent 30 minutes reading.
Mr. Yamamoto has a piece of plywood that is 15 1/2 ft. long and 12 3/4 ft. wide. He needs to cut the wood into 12 pieces for the students in his carpentry class. Mr. Yamamoto cuts the length into 4 equal pieces and the width into 3 equal pieces. What are the dimensions of each piece? Express the answers in simplest form.(1 point)
To find the dimensions of each piece, divide the length and width of the plywood by the number of pieces.
First, divide the length by 4:
15 1/2 ft. ÷ 4 = (31/2) ft. ÷ 4 = (31/2) ft. × (1/4) = 31/8 ft.
Each length piece will be 31/8 ft. long.
Then, divide the width by 3:
12 3/4 ft. ÷ 3 = (51/4) ft. ÷ 3 = (51/4) ft. × (1/3) = 51/12 ft.
Each width piece will be 51/12 ft. wide.
Therefore, each piece will have dimensions of 31/8 ft. by 51/12 ft.
wrong
I apologize for the mistake. Let's correct it.
To find the dimensions of each piece, we need to divide both the length and width of the plywood by the respective number of pieces.
First, let's divide the length (15 1/2 ft) into 4 equal pieces:
15 1/2 ft ÷ 4 = (31/2) ft ÷ 4 = (31/2) ft × (1/4) = 31/8 ft
Each length piece will be 31/8 ft long.
Next, let's divide the width (12 3/4 ft) into 3 equal pieces:
12 3/4 ft ÷ 3 = (51/4) ft ÷ 3 = (51/4) ft × (1/3) = 51/12 ft
Each width piece will be 51/12 ft wide.
Therefore, each piece will have dimensions of 31/8 ft by 51/12 ft.