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svlad2 [7]
2 years ago
6

The number of girls in Mrs. Manning’s classes was 12 less than twice the number of boys. She had a total of 108 students in her

classes. How many girls and how many boys are in Mrs. Manning’s classes?
Mathematics
1 answer:
FromTheMoon [43]2 years ago
4 0

40 boys and 68 girls

let's start with variables and an equation.

boys: x

girls: 2x - 12

and we know that boys and girls make up the class. so let's add the two expressions.

x + 2x - 12 = 108

3x - 12 = 108

    + 12     + 12

3x = 120

x = 40 boys

BUT x is only the number of BOYS in the class. so we have to find girls now. let's plug in our value of x into the girls' equation.

2x - 12 = # of girls

2(40) -12 = # of girls

80 - 12 = # of girls

68 girls

let's check our answer!

68 + 40 does in fact add to 108, therefore our answer is correct.

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Is it true that an irrational and a rational number is always a rational number
Vika [28.1K]

Answer:

no

Step-by-step explanation:

6 0
3 years ago
A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate off
GuDViN [60]

Correct question is;

A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate offered to a buyer, the number of sets sold will increase by 210 per week

A) Find the demand function (price p as a function of units sold x).

p(x)=______

(B) How large a rebate should the company offer the buyer in order to maximize its revenue?

$=_____

Answer:

A) p(x) = (-1/10)x + 590

B) Rebate = $170

Step-by-step explanation:

A) We are told that p(x) is the demand function and x is the number of TV sets sold per week.

Now, since for each $21 rebate offered, the number of sets sold increases by 210 per week, it means that the slope here of this demand function is; m = -21/210 = -1/10

Now, he has been selling 1400 TV sets a week at $450 each. This means; p(1400) = $450

Thus, the demand function will be;

p(x) - 450 = (-1/10)(x - 1400)

Expanding the RHS;

p(x) - 450 = (-1/10)x + 140

Add 450 to both sides to get;

p(x) = (-1/10)x + 140 + 450

p(x) = (-1/10)x + 590

B) Formula for revenue is;

R = price × quantity sold

Our demand function is p = (-1/10)x + 590

Making x the subject, we have;

x = 5900 - 10p

x is quantity sold.

Thus,

R = p(5900 - 10p)

R = 5900p - 10p²

Maximum price will occur at dR/dP = 0

Thus;

dR/dP = 5900 - 20p

At dR/dP = 0,we have;

20p = 5900

p = 5900/20

p = $280

Thus, rebate = 450 - 280 = $170

6 0
2 years ago
G = x-c/x solve for x
Elan Coil [88]

Answer:

x=\frac{c}{1-g}

Step-by-step explanation:

Step 1: Multiply both sides by x,

 gx=−c+x

Step 2: Add -x to both sides.

gx+−x=−c+x+−x

gx−x=−c

Step 3: Factor out variable x.

x(g−1)=−c

Step 4: Divide both sides by g-1.

\frac{x(g-1)}{g-1} =\frac{-c}{g-1\\}

x=\frac{c}{1-g}

Hope this helps!

5 0
3 years ago
Read 2 more answers
Select the correct answer. What is the range of this data? (3,3, 0, 8, 7, 10, 2, 6, 12, 0}
Natasha2012 [34]

Answer:

D: 12

Step-by-step explanation:

The range is the difference between the largest value in the date minus the smallest value in the data.

In this set of numbers given, the largest value is 12 and the smallest value is 0

so: 12-0 = 12

The range of this data is 12

8 0
3 years ago
You know that 15% of a number n is 12. How can you use this to find 30% of n? 45% of n? Explain.
Keith_Richards [23]
30% is 24
45% is 36
take 15% and multiply it by however much it takes to make the percentage than multiply that by 12
5 0
3 years ago
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