Solve Mixture Problems with Proportions Practice 23-24 Math 7 A, 6.23 / Use Proportional Relationships
the ratio of girls to boys in the school is 3 to 1. if there is a total of 400 students , how many are boys? the answer must be a whole number
(even though this is for the practice, I'll put the quick check answers here because math makes us all cry)
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1. 50 students
2. 50 minutes
3. 0.5 cup
4. 28 cups
5. 3 tsp
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hope this helps :D
-Sad-girl :)
To solve this problem, we can set up a proportion to find the number of boys in the school.
The ratio of girls to boys is given as 3 to 1. This means that for every 3 girls, there is 1 boy.
Let B represent the number of boys in the school.
Thus, we have the following proportion:
3 girls / 1 boy = (400 - B) girls / B boys
Now, we can cross-multiply and solve for B:
3B = 400 - B
4B = 400
B = 400 / 4
B = 100
Therefore, there are 100 boys in the school.
karen can read 10 pages and complete 15 math problems in 30 minutes. how long will it take her to do her homework if she has 30 pages to read and 45 math problems to complete? your answer should refer to the amount of time in minutes
First, we need to determine the rate at which Karen can read pages and complete math problems in 30 minutes.
We can set up a proportion using the rate:
10 pages / 15 math problems = 30 minutes / X
To find the time it takes for Karen to do her homework, we can set up another proportion:
30 pages / 45 math problems = X minutes / 1
Now, we can cross-multiply and solve for X:
10 / 15 = 30 / X
To find X, we divide both sides of the equation by (10/15):
X = (30 * 15) / 10
X = 45
Therefore, it will take Karen 45 minutes to complete her homework.
wrong
Apologies for the mistake. Let's correct it:
We can set up a proportion using the rate:
10 pages / 15 math problems = 30 minutes / X
To find the time it takes for Karen to do her homework, we can set up another proportion:
30 pages / 45 math problems = X minutes / 1
Now, we can cross-multiply and solve for X:
10 * X = 15 * 30
10X = 450
X = 450 / 10
X = 45
Therefore, it will take Karen 45 minutes to complete her homework with 30 pages to read and 45 math problems to complete.
45 is wrong
Apologies once again for the mistake. Let's correct it:
To solve this problem, we need to find the time it takes for Karen to complete her homework when she has 30 pages to read and 45 math problems to complete.
From the given information, we know that Karen can read 10 pages and complete 15 math problems in 30 minutes. This means that her rate of reading pages and completing math problems is constant.
Let's determine Karen's rate:
Rate of reading pages = 10 pages / 30 minutes = 1/3 pages per minute
Rate of completing math problems = 15 problems / 30 minutes = 1/2 problems per minute
Now, we can calculate the time it takes for Karen to do her homework:
Time to read 30 pages = (30 pages) / (1/3 pages per minute) = 90 minutes
Time to complete 45 math problems = (45 problems) / (1/2 problems per minute) = 90 minutes
Therefore, it will take Karen 90 minutes to complete her homework with 30 pages to read and 45 math problems to complete.