The sum of twice a number and 5 is 21. What is, №18010174, 24.10.2020 09:27

Mathematics

The sum of twice a number and 5 is 21. What is the number?

Step-by-step answer

P Answered by Specialist

Hello.

First, "twice a number" means we multiply 2 times that number.

Let the number be s.

Now, the sum of 2 times s and 5 is 21.

The product of 2 and s can be written like so:

$\sf{2s$

Now, the sum of 2s and 5 is 21:

$\sf{2s+5=21$

Subtract 5 from both sides:

$\sf{2s=21-5$

$\sf{2s=16}$

Now, divide both sides by 2:

$\Large\boxed{\sf{s=8}}$

I hope it helps.

Have a nice day.

$\boxed{imperturbability}$

Mathematics

1. The cost of petrol rises by 2 cents a liter. last week a man bought 20 liters at the old price. This week he bought 10 liters at the new price. Altogether, the petrol costs $9.20. What was the old price for 1 liter? 2. Teachers divided students into groups of 3. Each group of 3 wrote a report that had 9 pictures in it. The students used 585 pictures altogether. How many students were there in all? 3. Vera and Vikki are sisters. Vera is 4 years old and Vikki is 13 years old. What age will each sister be when Vikki is twice as old as Vera? 4.

Step-by-step answer

P Answered by Specialist

6

Answer for #1

Let the old price be
$
x
per liter. 10 liters would have cost a total of
$
10
x
.

The new price is
$
(
x
+
0.20
)
per liter. 10 liters would have cost
$
10
(
x
+
0.20
)
.

The total cost is
$
9.20
. So,

10
x
+
10
(
x
+
0.20
)
=
9.20
10
x
+
10
x
=
9.20
−
2
x
=
7.20
20
x
=
0.36

Thus, the old price was
$
0.36
per liter.

Mathematics

1. The cost of petrol rises by 2 cents a liter. last week a man bought 20 liters at the old price. This week he bought 10 liters at the new price. Altogether, the petrol costs $9.20. What was the old price for 1 liter? 2. Teachers divided students into groups of 3. Each group of 3 wrote a report that had 9 pictures in it. The students used 585 pictures altogether. How many students were there in all? 3. Vera and Vikki are sisters. Vera is 4 years old and Vikki is 13 years old. What age will each sister be when Vikki is twice as old as Vera? 4.

Step-by-step answer

P Answered by Master

6

Answer for #1

Let the old price be
$
x
per liter. 10 liters would have cost a total of
$
10
x
.

The new price is
$
(
x
+
0.20
)
per liter. 10 liters would have cost
$
10
(
x
+
0.20
)
.

The total cost is
$
9.20
. So,

10
x
+
10
(
x
+
0.20
)
=
9.20
10
x
+
10
x
=
9.20
−
2
x
=
7.20
20
x
=
0.36

Thus, the old price was
$
0.36
per liter.

History

1. Six less than twice a number A 6 - 2x B. 2x - 6 C. 6x-2 D. 2 - 6x 2. Five times the sum of a number and four. A. 5y + 4 B. 4(y + 5) c. 5+ 4y D. S(y + 4) 3. Which is the correct translation of the given 2(m-3)? A. Twice difference of 3 and m. C. Twice the difference of m and 3. B. Twice the sum of m and 3.. D. Twice the sum of m and 3. 4. Ten less than thrice the a numbers A 10 - 3b B. 3b - 10 C. 10b - 3 D. 3 - 10b 5. Given, m - 4, complete this: 4 A. minus B. diminished by a number. C. subtracted from D. decreased by 6. The ratio of 7 and a

Step-by-step answer

P Answered by Master

thanks I had already done this

History

1. Six less than twice a number A 6 - 2x B. 2x - 6 C. 6x-2 D. 2 - 6x 2. Five times the sum of a number and four. A. 5y + 4 B. 4(y + 5) c. 5+ 4y D. S(y + 4) 3. Which is the correct translation of the given 2(m-3)? A. Twice difference of 3 and m. C. Twice the difference of m and 3. B. Twice the sum of m and 3.. D. Twice the sum of m and 3. 4. Ten less than thrice the a numbers A 10 - 3b B. 3b - 10 C. 10b - 3 D. 3 - 10b 5. Given, m - 4, complete this: 4 A. minus B. diminished by a number. C. subtracted from D. decreased by 6. The ratio of 7 and a

Step-by-step answer

P Answered by Specialist

thanks I had already done this

Mathematics

Question 1: the sum of two consecutive even integers is 70. find the numbers. question 1 options: 28 and 32 30 and 40 33 and 37 34 and 36 question 2: cat is 5 less than twice dog s age. cat is 11 years old. find dog s age. question 2 options: 8 7 6 5 question 3: the sum of three consecutive numbers is 46. find the numbers. question 3 options: 19, 20, and 21 20, 21, and 22 21, 22, and 23 22, 23, and 24 question 4: what is the equation for the sum of three consecutive even numbers totaling 198. question 4 options: n+n+1+n+2=198 n+n+2+n+4=198 3n=198

Step-by-step answer

P Answered by Master

3

Question (1):
Assume that the first number is n. Since the two number are consecutive even numbers, this means that the second number is n + 2
We know that the sum of the two numbers is 70. This means that:
n + n + 2 = 70
2n + 2 = 70
2n = 68
n = 68/2
n = 34
This means that the two numbers are: 34 and 34+2 = 36 > last option

Question (2):
Assume dog's age is x. We know that cat's age is 5 less than twice dog's age. This means that:
cat's age = 2x - 5
We know that cat's age is 11, therefore:
11 = 2x - 5
11 + 5 = 2x
16 = 2x
x = 16/2 = 8
Dog's age is 8 > first option

Question (3):
The three numbers are consecutive. This means that we can assume the numbers to be n, n+1 and n+2. We know that their sum is 46. Therefore:
n + n + 1 + n + 2 = 46
3n + 3 = 46
3n = 43
n = 43/3
The three numbers are 43/3 , 46/3 and 49/3 > none of the given options in correct

Question (4):
The three consecutive numbers are all even. This means that we can assume the numbers to be n , n+2 and n+4
We know that their sum is 198. This means that:
n+n+2+n+4 = 198 > second option

Question (5):
The four consecutive numbers can be assumed as n, n+1 , n+2 and n+3. We know that their sum is 86. Therefore:
n + n+1 + n+2 + n+3 = 86 > third option

Question (6):
Assume the width is w. We know that the length is 15 cm greater than the width. This means that:
length = w + 15
Now, we have:
perimeter = 2(length + width)
150 = 2 (15 + w + w)
75 = 15 + 2w
60 = 2w
w = 60/2
w = 30 cm
This means that:
length = 15 _ 30 = 45 cm
Based on the above, the dimensions of the rectangle are:
length = 45 cm and width = 30 cm > first option

Question (7):
Assume original price before taxes is x
Total price = original price + taxes
825 = x + 0.1x = 1.1 x
x = 825/1.1
x = $750 > second option

Question (8):
Assume cost of helmet is x and that cost of bicycle is 5x. We know that the total is 240. This means that:
240 = x + 5x = 6x
x = 240/6
x = 40
This means that:
price of helmet = $40
price of bicycle = 5(40) = $200
> first option

Hope this helps :)

Mathematics

Question 1: the sum of two consecutive even integers is 70. find the numbers. question 1 options: 28 and 32 30 and 40 33 and 37 34 and 36 question 2: cat is 5 less than twice dog s age. cat is 11 years old. find dog s age. question 2 options: 8 7 6 5 question 3: the sum of three consecutive numbers is 46. find the numbers. question 3 options: 19, 20, and 21 20, 21, and 22 21, 22, and 23 22, 23, and 24 question 4: what is the equation for the sum of three consecutive even numbers totaling 198. question 4 options: n+n+1+n+2=198 n+n+2+n+4=198 3n=198

Step-by-step answer

P Answered by Specialist

3

Question (1):
Assume that the first number is n. Since the two number are consecutive even numbers, this means that the second number is n + 2
We know that the sum of the two numbers is 70. This means that:
n + n + 2 = 70
2n + 2 = 70
2n = 68
n = 68/2
n = 34
This means that the two numbers are: 34 and 34+2 = 36 > last option

Question (2):
Assume dog's age is x. We know that cat's age is 5 less than twice dog's age. This means that:
cat's age = 2x - 5
We know that cat's age is 11, therefore:
11 = 2x - 5
11 + 5 = 2x
16 = 2x
x = 16/2 = 8
Dog's age is 8 > first option

Question (3):
The three numbers are consecutive. This means that we can assume the numbers to be n, n+1 and n+2. We know that their sum is 46. Therefore:
n + n + 1 + n + 2 = 46
3n + 3 = 46
3n = 43
n = 43/3
The three numbers are 43/3 , 46/3 and 49/3 > none of the given options in correct

Question (4):
The three consecutive numbers are all even. This means that we can assume the numbers to be n , n+2 and n+4
We know that their sum is 198. This means that:
n+n+2+n+4 = 198 > second option

Question (5):
The four consecutive numbers can be assumed as n, n+1 , n+2 and n+3. We know that their sum is 86. Therefore:
n + n+1 + n+2 + n+3 = 86 > third option

Question (6):
Assume the width is w. We know that the length is 15 cm greater than the width. This means that:
length = w + 15
Now, we have:
perimeter = 2(length + width)
150 = 2 (15 + w + w)
75 = 15 + 2w
60 = 2w
w = 60/2
w = 30 cm
This means that:
length = 15 _ 30 = 45 cm
Based on the above, the dimensions of the rectangle are:
length = 45 cm and width = 30 cm > first option

Question (7):
Assume original price before taxes is x
Total price = original price + taxes
825 = x + 0.1x = 1.1 x
x = 825/1.1
x = $750 > second option

Question (8):
Assume cost of helmet is x and that cost of bicycle is 5x. We know that the total is 240. This means that:
240 = x + 5x = 6x
x = 240/6
x = 40
This means that:
price of helmet = $40
price of bicycle = 5(40) = $200
> first option

Hope this helps :)

Mathematics

(25 points) PLEASE HELP! Gotta get this done before my mom comes home 1. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag? A. Cashews: 0.10 lb.; peanuts: 0.40 1b. B. Cashews: 0.42 lb.; peanuts: 0.08 1b. C. Cashews: 0.40 lb.; peanuts: 0.10 1b D. Cashews: 0.27 lb.; peanuts: 0.23 1b. E. Cashews: 0.23 lb.; peanuts: 0.27 1b. F. Cashews: 0.08 lb.;

Step-by-step answer

P Answered by Master

4

Hey, the only one I could figure out was no. 2 and 3. Sorry.

2. D) Red roses: 126; pink roses: 162
3. C) S+H=46 H=S-2

I hope you found this helpful :)

Mathematics

(25 points) PLEASE HELP! Gotta get this done before my mom comes home 1. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag? A. Cashews: 0.10 lb.; peanuts: 0.40 1b. B. Cashews: 0.42 lb.; peanuts: 0.08 1b. C. Cashews: 0.40 lb.; peanuts: 0.10 1b D. Cashews: 0.27 lb.; peanuts: 0.23 1b. E. Cashews: 0.23 lb.; peanuts: 0.27 1b. F. Cashews: 0.08 lb.;

Step-by-step answer

P Answered by Master

4

Hey, the only one I could figure out was no. 2 and 3. Sorry.

2. D) Red roses: 126; pink roses: 162
3. C) S+H=46 H=S-2

I hope you found this helpful :)

Mathematics

8. The larger of two numbers is 8 more than twice the smaller. The sum of the numbers is 35. Find the numbers. * a.) 7,28 b.) 9,26 c.) 13.5, 21.5 d.) 13.5, 35

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

Givens

smaller number = x

Larger number = 2x + 8

Sum = 35

Equation

x + 2x + 8 = 35

Solution

3x + 8 = 35

3x = 35 - 8

3x = 27

x = 9

The smaller number = 9

The larger number = 2*9 + 8 = 26

My answers aren't in the list. Are you sure the numbers in the list are correct?

The sum of twice a number and 5 is 21. What is the number?

Step-by-step answer

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