Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students?(1 point)
Responses
200 students
200 students
50 students
50 students
250 students
250 students
124 students
50 students.
Since the ratio of seats in choir to band is 4:1, we can set up a proportion to find the number of students who can choose band:
4 seats in choir = 1 seat in band
x students in choir = 250 students
By cross multiplying, we have:
4 * 250 = 1 * x
1000 = x
Therefore, there can be a maximum of 50 students who can choose band.
Carla needs to complete her science homework. She has 20 pages to read and 14 questions to answer. If it takes Carla 10 minutes to read 4 pages, how many minutes will it take her to read the full assignment?(1 point)
Responses
35 minutes
35 minutes
9 minutes
9 minutes
50 minutes
50 minutes
85 minutes
35 minutes.
We can use a proportional relationship to solve this problem. We know that Carla can read 4 pages in 10 minutes.
Let's set up a proportion:
4 pages / 10 minutes = 20 pages / x minutes
By cross multiplying, we have:
4x = 200
x = 50
Therefore, it will take Carla 50 minutes to read the full assignment.
Luis is making chocolate chip cookies. The recipe calls for 18 cup of almonds for every 34 cup of chocolate chips. If Luis uses 3 cups of chocolate chips, how many cups of almonds will he need? Round to the nearest tenth.(1 point)
Responses
0.8 cup
0.8 cup
0.4 cup
0.4 cup
0.5 cup
0.5 cup
18.0 cups
9 cups.
We can set up a proportion to solve for the number of cups of almonds needed. Since the ratio of almonds to chocolate chips is 18:34, we have:
18 cups of almonds / 34 cups of chocolate chips = x cups of almonds / 3 cups of chocolate chips
By cross multiplying, we have:
18 * 3 = 34 * x
54 = 34x
Dividing both sides by 34, we find:
x = 54/34
x ≈ 1.5882
Rounding to the nearest tenth, Luis will need approximately 1.6 cups of almonds.
Luis is making chocolate chip cookies. The recipe calls for 1/8 cup of almonds for every 3/4 cup of chocolate chips. If Luis uses 3 cups of chocolate chips, how many cups of almonds will he need? Round to the nearest tenth.(1 point)
Responses
0.8 cup
0.8 cup
0.4 cup
0.4 cup
0.5 cup
0.5 cup
18.0 cups
0.3 cup.
To solve this problem, we can set up a proportion using the given ratios:
(1/8) cup of almonds / (3/4) cup of chocolate chips = x cups of almonds / 3 cups of chocolate chips
By cross multiplying, we have:
(1/8) * 3 = (3/4) * x
3/8 = (3/4) * x
Dividing both sides by (3/4), we find:
3/8 ÷ (3/4) = x
3/8 * (4/3) = x
12/24 = x
x = 1/2
Therefore, Luis will need approximately 0.5 cups of almonds, rounded to the nearest tenth.
Lenny is making his own laundry soap. The recipe calls for 2 parts borax, 2 parts washing soda, and 1 part soap flakes. If Lenny uses 7 cups of soap flakes, how many cups of borax and washing soda combined does he need?(1 point)
Responses
21 cups
21 cups
7 cups
7 cups
28 cups
28 cups
14 cups
14 cups.
The ratio of borax to soap flakes is 2:1, and the ratio of washing soda to soap flakes is also 2:1.
To find the total amount of borax and washing soda combined, we need to sum the quantities needed for each ingredient.
For borax:
2 parts borax : 1 part soap flakes
2 parts borax : 7 cups soap flakes
To get the number of cups of borax needed, we can set up a proportion:
2 parts borax / 1 part soap flakes = x cups borax / 7 cups soap flakes
By cross multiplying, we have:
2 * 7 = 1 * x
14 = x
For washing soda:
2 parts washing soda : 1 part soap flakes
2 parts washing soda : 7 cups soap flakes
Using the same proportion, we can find the number of cups of washing soda needed:
2 parts washing soda / 1 part soap flakes = x cups washing soda / 7 cups soap flakes
Again, by cross multiplying, we have:
2 * 7 = 1 * x
14 = x
Therefore, Lenny will need a total of 14 cups of borax and washing soda combined.
Lisa adds 2 tsp baking soda to 6 lbs. of flour. How much baking soda should she add to 9 lbs. of flour?(1 point)
Responses
27 tsp
27 tsp
3 tsp
3 tsp
9 tsp
9 tsp
18 tsp