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Mathematics High School

Alice has 12 more trees in her garden than Stephen has. After Stephen planted

Alice has 12 more trees in her garden than Stephen has. After Stephen planted 10 more trees and Alice dug out 4, together they had 36 trees. How many trees did each of them have at the beginning?

2 months ago

Solution 1

Guest

Guest #1627358

2 months ago

Answer:

Stephen has 9 trees

Alice has 21 trees

Step-by-step explanation:

At the beginning:

Stephen = x trees

Alice = x + 12 trees

At the end:

Alice = (x + 12) - 4 trees

Stephen = x + 10 trees

Total = 36

Then

$((x+12)-4)+(x+10)=36\\ \\(x+12-4)+(x+10)=36\\ \\(x+8)+(x+10)=36\\ \\x+8+x+10=36\\ \\2x+18=36\\ \\2x+18-18=36-18\\ \\2x=18\\ \\x=9$

Stephen - 9 trees

Alice - 9 + 12 = 21 trees

Solution 2

Guest

Guest #1627359

2 months ago

Answer:

Stephen has 9 trees

Alice has 21 trees

Step-by-step explanation:

Alice has 12 more trees in her garden than Stephen has. After Stephen planted 10 more trees and Alice dug out 4, together they had 36 trees. How many trees did each of them have at the beginning?

📚 Related Questions

Question

Find any real solutions for the following quadratic equations. 2 x2 - 8 = 0 x2 = -5

Solution 1

Hello,
I) 2(x²-4)=0
==>(x-2)(x+2)=0
==>x=2 or x=-2

II)
No real solutions.

Question

20 POINTS!! Assume the exponential growth model A(t)=A subscript 0 e superscript kt and a world population of 6.7 billion in 2005. If the population must stay below 21billion during the next 100 years, what is the maximum acceptable annual rate of grow

Solution 1

Answer:

0.010423315 x 109 = 1.04 x 107 people

Step-by-step explanation:

(19 x 109) = (6.7 x 109) (e100k)

and solve for k

(19 x 109) / (6.7 x 109) = e100k

2.835820896 = e100k

ln 2.835820896 = ln e100k

ln 2.835820896 = 100k

k = (ln 2.835820896) / 100

Question

Samuel bought a jacket for $16 in January. The cost of the jacket increased to $24 in September. What percent of the original price is the new price? A. 110% B. 120% C. 150% D. 180%

Solution 1

Answer:

The answer is option C=150%

Step-by-step explanation:

Original cost of the jacket=$16 in January

Final cost of jacket=$24 in September

What percentage must of the original price is the new?

The new price=the original price×(A percentage)

Where the new price=$24, the original price=$16, and the percentage=(x/100)

24=16×x/100

x=(24×100)/16=150%

The answer is 150%

Solution 2

Answer:

c

Step-by-step explanation:

Question

Gourmet Pretzels bakes soft pretzels on an assembly line. It currently bakes 800 pretzels each eight-hour shift. If the production is increased to 1,200 pretzels each shift, then productivity will have increased by: Group of answer choices a.33 percent. b.50 percent. c.67 percent. d.25 percent.

Solution 1

Percent counts the quantity per 100 (cent=100). The productivity of Gourmet Pretzels increased(in percentage) is given by: Option b. 50%

How to find the percentage from the total value?

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

$\dfrac{a}{100} \times b$

For the given case, increment in her productivity is obtained by

Increment = New productivity - previous productivity

Increment amount = 1200 - 800 = 400 pretzels each shift

Let it is p% of the previous productivity.

Then,

$400 = \dfrac{800}{100} \times p = 8 \times p\\\text{Dividing both the sides by 8}\\\\p =\dfrac{400}{8} = 50$

Her productivity increased by 50% (compared to previous productivity).

Hence, the productivity of Gourmet Pretzels increased(in percentage) is given by: Option b. 50%

Learn more about percentage here:

brainly.com/question/11549320

Solution 2

Answer:

Change in productivity will be 50%

So option (b) will be correct option

Step-by-step explanation:

It is given that it takes 8 hour to bake 800 pretzels

And there is a shift of 8 hours

So hourly production = $\frac{800}{8} =100$

Now the production is increases to 1200

Now hourly production = $\frac{1200}{8}=150$

So change in productivity = $\frac{150-100}{100}=50$ %

So option (b) will be correct answer

Question

Rosa says that to find how many tortillas she can fill, she first finds find how many 1/3 cups are in 8 cups. What else must Rosa do to find how many tortillas she can fill?

Solution 1

She can divide the 8 cups by the 1/3 cups

Step-by-step explanation:

The next step will be to divide 8 cups by 1/3 cups

This will be:

= 8÷1/3

=8*3/1-------------dividing by a fraction is the same as multiplying by its reciprocal

= 24

There are 24 1/3cups in 8 cups.

Learn More

Division brainly.com/question/1060802

Keywords : tortillas

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Solution 2

Answer:

Rosa divides the result of $8\div \frac{1}{3}$ by 2

Step-by-step explanation:

We are given that

Rosa puts vegetable mixture in tortilla= $\frac{2}{3}$ cup

She has total vegetable mixture=8 cups

We have to find the what else must Rosa do to find how many tortillas she can fill.

She first finds how many 1/3 cups in 8 cups of vegetable mixture.

Number of 1/3 cups of vegetable mixture= $8\div\frac{1}{3}$

Number of 1/3 cups of vegetable mixture= $24$

Now, we will find number of tortillas by dividing 24 by 2

She can fill tortillas of vegetable mixture= $24\div 2=12$

Hence,Rosa divides the result of $8\div \frac{1}{3}$ by 2.

Question

In a soccer game, 1/6 of the players on Team A and 1/5 of the players on Team B score a goal. A total of 3 players on Team A and 3 players on Team B score a goal. How many players are on each team?

Solution 1

Answer:

Team A: 18 players.

Team B: 15 players.

Step-by-step explanation:

Goal scored:

Team A: $\frac{1}{6}$ ; which equals 3 players.

Team B: $\frac{1}{5}$ ; which equals 3 players.

So, if 1/6 equals 3 players, what is the total, we can see this as a specific expression: $\frac{1}{6} x=3$ ; being the variable the total number of players, solving this equation: $x=3.6=18$

Doing the same process for Team B:

$\frac{1}{5}x=3\\ x=3.5=15$

Hence, Team A has 18 players, and Team B has 15 players.

Question

Every cubic millimeter of blood contains about 7500 white blood cells. A count less than 1500 above this number is still considered healthy. Is white cell count of 8750 considered healthy. Explain

Solution 1

Answer:

The white cell count of 8750 is considered healthy.

Step-by-step explanation:

The question calls for any white cell count below 1500 above 7500 to be considered healthy. So, by adding the number 1500 to 7500 we find that the upper limit for being healthy is 9000 white blood cells per cubic millimeter of blood. This all can be represented mathematically with the following:

If:

$7000 \leq x \leq 9000$

Then

White blood cell count 'x' is healthy.

Else if:

$x < 7500$ or $x > 9000$

Then

White blood cell count 'x' is not healthy.

Now let's test the white cell count of 8750.

Does it fall between 7500 and 9000?

$7500 \leq 8750 \leq 9000$

This checks out so the answer is yes: White blood cell count '8750' is healthy.

Question

Use the GCF to factor this expression: 90x + 4

Solution 1

90x + 4
Factor out GCF
2 ( 45x + 2)

Question

The data set represents the number of rings each person in a room is wearing. 0, 2, 4, 0, 2, 3, 2, 8, 6 What is the interquartile range of the data?

Solution 1

Answer: 4

Step-by-step explanation:

First arrange the given data in ascending order :-

$0,0,2,2,2,3,4,6,8$

Number of terms = 9

Second quartile =Median= $\dfrac{9+1}{2}=5^{th}\ term=2$

Now, the first quartile $Q_1$ =The median for the lower half of data

= Mean of 2nd term and 3rd term

$=\frac{0+2}{2}=1$

The third quartile $Q_3$ =The median for the upper half of data

= Mean of 7th term and 8th term

$=\frac{2+8}{2}=5$

Now, Interquartile range = $Q_3-Q_1=5-1=4$

Hence, the interquartile range of the data =4.

Solution 2

Answer:

(C) 4

Step-by-step explanation:

♥☺

Question

The first 7 Fibonacci numbers are 1,1,2,3,5,8,13,... each number in the sequence is the sum of the previous two numbers. Thus 13=8+5 and 8=5+3. (a) What are the eighth and ninth Fibonacci numbers? (b) What do you get if you subtract the 8th Fibonacci number from the 9th Fibonacci number?

Solution 1

Answer:

A: 21, 34; B: 13

Step-by-step explanation:

Part A:

OK to find this answer you just need to add the 6th and 7th terms together:

$8 + 13 = 21\\$

Then you add your new 8th term (this term being 21) to your 7th term to get the ninth term:

$13 + 21 = 34$

Part B:

If you subtract the 9th term by the 8th term you'll get the 7th term. This is because to get the 9th term the 7th and 8th terms needed to be added together. So you'd get 13 by subtracting the 8th term from the 9th term because it is the 7th term.

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