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3 years ago

The sum of 3 consecutive odd integers is 18 less than five times the middle number. Find the three integers

Mathematics

1 answer:

Andreyy893 years ago

8 0

n, n + 2, n + 4 - three consecutive odd ntegers

n + (n + 2) + (n + 4) = 5(n + 2) - 18 |use distributive property

n + n + 2 + n + 4 = (5)(n) + (5)(2) - 18

3n + 6 = 5n + 10 - 18

3n + 6 = 5n - 8 |subtract 6 from both sides

3n = 5n - 14 |subtract 5n from both sides

-2n = -14 |divide both sides by (-2)

n = 7

n + 2 = 7 + 2 = 9

n + 4 = 7 + 4 = 11

Answer: 7, 9, 11.

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The ratio of boys to girls in a group is 7:1. If there are 66 more boys than girls, work out how many girls there are

nevsk [136]

Answer:11

Step-by-step explanation:

Boys : girls=7:1

Sum of ratio=7+1=8

Let them number of girls be y

Then they number of boys=y+66

Total number of pupils=y+y+66

Total number of pupils=2y+66

Number of girls=(girls ratio)/(sum of ratio) x (total number of pupils)

y=1/8 x (2y+66)

Cross multiply

y x 8=2y + 66

8y=2y + 66

Collect like terms

8y-2y=66

6y=66

Divide both sides by 6

6y/6=66/6

y=11

The number of girls is 11

4 0

3 years ago

The question is in the attached file.

Readme [11.4K]

The answer is in the attached file.

6 0

3 years ago

It took 30 minutes for Melinda to run 4 miles<br> (Find the unit rate and explain what they mean)

zhannawk [14.2K]

Each mile took 7.5 minutes. So we did this by dividing 30 by 4. Hope this helped you :)

5 0

3 years ago

Read 2 more answers

Peter takes16 minutes longer to mow the lawn by himself than Charles . Together they can mow the lawn in 18 minutes. How long wi

lapo4ka [179]

Answer:

about 29.7 minutes

Step-by-step explanation:

If it take c minutes for Charles to mow the lawn by himself, it takes c+16 minutes for Peter. The two of them working together can mow in one minute this fraction of the entire lawn:

1/c + 1/(c+16) = 1/18

Multiplying by 18c(c+16), we get ...

18(c +16) + 18(c) = c(c+16)/18

36c +288 = c^2 +16c

c^2 -20c = 288 . . . . . subtract 36c

c^2 -20c +100 = 388 . . . . . add (20/2)^2 = 100 to complete the square

(c -10)^2 = 388

c = 10 +√388 ≈ 29.6977 . . . . . take the positive square root

It takes Charles about 29.7 minutes to mow the lawn by himself.

7 0

3 years ago

quadrilateral paid is a rectangle whose diagonals have the endpoints p(-3, -2)i(4, -7) and a(4, -2)d(-3, -7). find the diagonals

julia-pushkina [17]

Answer:

The intersection point of diagonals is (0.5,-4.5).

Step-by-step explanation:

The end points of first diagonal are p(-3, -2) and i(4, -7).

The end points of second diagonal are a(4, -2) and d(-3, -7).

If a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of first diagonal is

$y-(-2)=\frac{-7-(-2)}{4-(-3)}(x-(-3))$

$y+2=\frac{-5}{7}(x+3)$

$7y+14=-5(x+3)$

$7y+14=-5x-15$

$5x+7y=-29$ .... (1)

The equation of second diagonal is

$y-(-2)=\frac{-7-(-2)}{-3-4}(x-4)$

$y+2=\frac{-5}{-7}(x-4)$

$7y+14=5(x-4)$

$7y+14=5x-20$

$5x-7y=34$ .... (2)

Add equation (1) and (2),

$10x=5$

$x=0.5$

Put this value in (1).

$5(0.5)+7y=-29$

$y=-4.5$

The intersection point of diagonals is (0.5,-4.5).

3 0

3 years ago