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3 years ago

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The ratio of girls to boys in the junior high band is 5 to 7. At the beginning of year, there were 72 students in the band. By t

he end of the year, the ratio of girls to boys was 3 to 4. If there are now 48 boys in the band, how many girls joined the band during the school year?

2 answers:

Andre45 [30]3 years ago

8 0

Answer:

Your answer will be 36

Step-by-step explanation:

I know that because there were 30 girls in the beginning of school and 6 girls joined band with is 36

rusak2 [61]3 years ago

7 0

Ratio is 5girls:7boys with total 72 students
5+7= 12
72➗12= 6
6(5:7)= 30 girls : 42 boys

New ratio is 3:4 with 48 boys

48➗4= 12

So for girls 3x12= 36

So started with 30 girls ended with 36 girls... 6 girls joined band during the school year.

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a positive integer is twice another. The sum of the reciprocals of the two positive integers is frac 3/16, find the two integers

gizmo_the_mogwai [7]

Step-by-step explanation:

Let $x$ be the smallest integer

Let $2x$ be the larger integer

As the sum of the reciprocals of the two positive integers is frac 3/16

So,

$\frac{1}{x}\:+\:\frac{1}{2x}\:=\:\frac{3}{16}$

$\mathrm{Multiply\:by\:LCM=}16x$

$\frac{1}{x}\cdot \:16x+\frac{1}{2x}\cdot \:16x=\frac{3}{16}\cdot \:16x$

Simplify

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$\mathrm{Switch\:sides}$

$3x=24$

$\mathrm{Divide\:both\:sides\:by\:}3$

$\frac{3x}{3}=\frac{24}{3}$

$x=8$

So,

$2x=16$

<h2>Verification:</h2>

$\frac{1}{8}\:+\:\frac{1}{16}$

$\mathrm{Least\:Common\:Multiplier\:of\:}8,\:16:\quad 16$

$=\frac{2}{16}+\frac{1}{16}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

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Therefore,

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Keywords: word problem , integer

Learn more about solving integer word problem from brainly.com/question/10905225

#learnwithBrainly

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3 years ago

What are the solutions to x^2 + 8x + 7 = 0

Oksana_A [137]

So to solve this you need to reverse factor this problem

x^2 + 8x + 7 = 0

The common formula is this for factoring ax^2 + bx + c

Now you have to think what multplties to "c" and adds up to "b".

So in this case it's 7 x 1 = 7 and 7 + 1 = 8

So you set it up like this

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So now you can check the factors by multiplying them together and see if it gets your original equation which is does.

So finally to get the answers you need to set each parenthesis to 0 and solve for x.

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and we get x = -1 and - 7

You can also plug these two answers back into your original equation to see if it equals 0.

If you have any questions please feel free to comment

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