MATHEMATICS HIGH SCHOOL

Solve the following problem first using a tape diagram and then using an equation: In a school choir, 1/2 of the members were girls. At the end of the year, 3 boys left the choir, and the ratio of boys to girls became 3:4. How many boys remained in the choir?

Answers

Answer 1

Answer:

Answer: 9 boys remained in the choir.

Step-by-step explanation:

Let x be the number of of boys and y be the number of girls.

In a school choir, 1/2(half) of the members were girls.

i.e $x=y$ (1)

At the end of the year, 3 boys left the choir, and the ratio of boys to girls became 3:4.

$(x-3)/(y)=(3)/(4)\n\n\Rightarrow\ 4(x-3)=3(y)\n\n\Rightarrow\ 4x-12=3y$

Put y= x from (1), we get

$4x-12=3x\n\n\Rightarrow\ 4x-3x=12\n\n\Rightarrow\ x=12$

Thus , the number of boys : x= 12

Boys remained in the choir = 12-3=9

Related Questions

Describe the translation of Point A (3, -8) to A'(-4,-5).
Choose all the numbers that are multiples of 4.6 10 12 20 24 30 36
Craig is considering four loans. Loan L has a nominal rate of 8.254%, compounded daily. Loan M has a nominal rate of 8.474%, compounded weekly. Loan N has a nominal rate of 8.533%, compounded monthly. Loan O has a nominal rate of 8.604%, compounded yearly. Which of these loans will offer Craig the best effective interest rate?
Which pair of numbers is relatively prime? A.18 and 45B.26 and 91C.10 and 33D.14 and 63
Please help! Fast−6(2x−4)≤30.

Is 6x = y proportional

Answers

Answer:

Yes, it is proportional

Step-by-step explanation:

In a proportional relationship, the ratio between the two variables remains constant.

If you divide both sides of the equation by 6

x = y/6

This shows that x is directly proportional to y with a constant of 1/6.

So, it is proportional.

Sandy walked around her neighborhood. In ½ hour, she walked 1 and 1/5 miles. What is Sandy’s rate in miles per hour?

Answers

Answer:

2 2/5 miles per hour

Step-by-step explanation:

We want to find the miles per hour

Changing the miles to an improper fraction

1 1/5 = ( 5*1+1)/5 = 6/5 miles

6/5 miles

Divide by the number of hours 1/2

6/5 ÷ 1/2

Copy dot flip

6/5 * 2/1

12/5

Change back to a mixed number

2 2/5 miles per hour

She walked 2 2/5 mph

How to solve for y if the equation is y=5/2x + 5 if x is zeroplease show step by step how to solve

Answers

$y=(5)/(2)\cdot0+5\ny=0+5\ny=5$

Q, y=5/2x+x if x is zero

An, ( y=5/2×0+5 ) as you know if i multiply number to zero you get zero so "x" change to the zero you get
( y=0+5 )= ( y=5 ) that is your answer

Simonne used the following steps to simplify the given expression. 12 - 3(-2x + 4) Step 1: 12 + (–3)·(–2x) + (–3)·(4)
Step 2: 12 + 6x + (–12)
Step 3: 12 + (–12) + 6x
Step 4: 0 + 6x Step 5: 6x

What property of real numbers was used to transition from Step 3 to Step 4?
A. identity property of addition
B. inverse property of addition
C. associative property of addition
D. commutative property of addition

Answers

inverse property of addition

B: inverse property of addition

3p4 ( 4p4 + 7p3 + 1 )

Answers

$3p^4 (4p^4 + 7p^3 + 1) \n \n 3p^4 * 4p^4 + 3p^4 * 7p^3 + 3p^4 \n \n 3 * 4p^4p^4 + 3p^4 * 7p^3 + 3p^4 \n \n 3 * 4p^(4 + 4) + 3p^4 * 7p^3 + 3p^4 \n \n 3 * 4p^8 + 3p^4 * 7p^3 + 3p^4 \n \n 12p^8 + 3p^4 * 7p^3 + 3p^4 \n \n 12p^8 + 3 * 7p^4p^4 + 3p^4 \n \n 12p^8 + 3 * 7p^(4 + 3) + 3p^4 \n \n 12p^8 + 3 * 7p^7 + 3p^4 \n \n 12p^8 + 21p^7 + 3p^4$

The answer is: 12p^8 + 21p^7 + 3p^4.

3p⁴(4p⁴ + 7p³ + 1)
3p⁴(4p⁴) + 3p⁴(7p⁴) + 3p⁴(1)
12p⁸ + 21p⁷ + 3p⁴

The volume of a solid right pyramid with a square base is v units3 and the length of the base edge is y units. which expression represents the height of the pyramid? units (3v – y2) units (v – 3y2) units units

Answers

we know that

The volume of a solid right pyramid with a square base is equal to

$V=(1)/(3)*[ area\ of\ the\ base]*height$

area of the base is the area of a square

$area\ of\ the\ base=y^(2)\ units^(2)\nV=v\ units^(3)$

Substitute the values in the formula of volume

$v=(1)/(3)*[ y^(2)]*height$

solve for the height

$v=(1)/(3)*[ y^(2)]*height\n \nheight=(3v)/(y^(2))\ units$

therefore

the answer is

$height=(3v)/(y^(2))\ units$

3v/y² units

Further explanation

Given:

The volume of a solid right pyramid with a square base is v units³
The length of the base edge is y units.

Question:

Which an expression represents the height of the pyramid?

The Process:

We will solve the problem of a geometric solid.

Let us recall the formula of volume of a right pyramid:

$\boxed{ \ V = (1)/(3) * base \ area * height \ }$

Because the base is square, we use the formula for square area, i.e., side times side.

Let us find out the height of the pyramid.

$\boxed{ \ Height = (3v)/(y * y) \ }$

Thus, an expression represents the height of the pyramid is $\boxed{\boxed{ \ (3v)/(y^2) \ }}$ units

Learn more

What is the volume of each prism? brainly.com/question/414021
The volume of rectangular prism brainly.com/question/11613210
Express the volume of the box as a function of the length of the edge of the base. What is its domain? brainly.com/question/4925904

Keywords: the volume of a solid right pyramid, a square, the length of the base edge, an expression, represent, the height, the formula, a geometric solid, units

Other Questions

David bought a car for 5000$ for how much should he sell it if he wants 10% profit from it

Baseball cards come on packages of 8 and 12. Brighton bought some of each type for a total of 72 baseball cards. How many of each package did he buy?

Equivalent ratios for 5:13

Point W was translated as follows W(-4,7) -> W'(-2,4) a student wrote the algebraic rule to describe the translation as (x,y)->(x-3,y+2) evaluate the students answer