Elijah was six times as old as his son. In twelve years he will be twice as old as his son. How old are they now

Answers

Answer 1

To solve this, we need to turn this word problem into a system of linear equations. To do this, let's use x to stand for Mr. Fontana's age, and y to stand for his son's age.

The first sentence states that eight years ago, Mr. Fontana was six times as old as his son.

eight years ago = x - 8

Fontana was six times as old as his son = 6(y - 8). Remember, we need subtract 8 from his son's age, which is why I wrote it as 6(y - 8), and his father was 6 times his son's age 8 years ago, which is why I multiplied 6 by y - 8.

Now, putting this all together gives us our first equation:

x - 8 = 6(y - 8)

We can now rewrite this equation in standard form:

x - 8 = 6y - 48 ----->

x - 6y = -48 + 8 ----->

x - 6y = -40 <----- this is our first linear equation

To find our second, we need to turn the second sentence into an equation. It says that in 12 years, Mr. Fontana will be twice as old as his son:

x + 12 = 2(y + 12)

Now, we need to rewrite this equation in standard form:

x + 12 = 2y + 24 ----->

x - 2y = 24 - 12 ----->

x - 2y = 12 <----- this is our second linear equation. We now have our system of equations:

x - 6y = -40

x - 2y = 12

Now we can find the father's age (x) and his son's age (y). First, multiply the second equation by -1, giving us:

x - 6y = -40

-x + 2y = -12

Now we can add both equations together:

x - x - 6y + 2y = -40 + -12 ----->

-4y = -52

Solve for y, by dividing both sides of the equation by -4, giving us:

y = 13

So, now we know the son's age: 13

To find the father's age, replace y in either the first equation or the second equation, with 13. Let's use the first equation:

x - 6(13) = -40 ----->

x - 78 = -40 ----->

x = 78 - 40 ----->

x = 38

Therefore, Mr. Fontana is 38 years old and his son is 13 years old.


Related Questions

Describe the location of the polnt having the following coordinates. abscissa and ordinate have the same sign
Quadrant II or Quadrant IV
Quadrant II or Quadrant III
Quadrant or Quadrant IV
Quadrant I or Quadrant III​

Answers

Answer:

i think its D

Step-by-step explanation:

hope this helps!

some help, I need some answers

Answers

Step-by-step explanation:

here

10^2=8^2+X^2

X^2=100-64

X=√36

X=6

2/5 of 40 I need help​

Answers

Answer:

32. A.

Step-by-step explanation: because i did 4/5 of 40 and got 32.

How many pennies dose Michael please help please I need your help please please please please help

Answers

Answer: He has 91, to figure this out count everything in top row which is 13 and then count everything in left row only which is 7 and 13 x 7 is 91

Step-by-step explanation:

Solve the inequality for x.
9x - 7 < 7x - 25

Answers

Answer:

x<-9

Step-by-step explanation:

subtract the 7x from the right side to bring it over to the left side to get:

2x-7<-25

then add the 7 from the left side to bring it over to the right side to get:

2x<-18 and then divide both sides by 2 to get the final inequality to be:

x<-9

Answer: x < -9Step-by-step explanation:9x - 7 < 7x - 25=> 9x - 7x < 7 - 25=> 2x < -18=> x < -9Conclusion:

Therefore, the solved inequality is x < -9.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Explain this picture ​

Answers

Answer:

It's A bar graph but I got to see the question to be for sure but its a bar graph and it helps you  measure rates of things from numbers , months , years etc .

Step-by-step explanation:

Find the perimeter of a semicircle with a radius of 9 in.
Please explain and be accurate.

Answers

Answer:

9π + 18

Step-by-step explanation:

The circumference of a circle is pi times diameter, so 9 x 2 = 18 inches, which is the diameter. That will be the flat side of the semicircle. Then the circumference of the whole circle will be 18π. To find the curved side of the semi-circle, divide this by 2, so you get 9π. Therefore the answer is 9π + 18. The rough answer to 3 decimal places is 46.274

(SAT Prep) Find the value of x

Answers

Answer:

x = 36

Step-by-step explanation:

3x+2x=180

5x=180

x=36

Answer:

x=36 degrees

Step-by-step explanation:

A sports store has jerseys representing the seven Canadian NHL teams and the eight Canadian CFL teams. Five of these jerseys have to be chosen for display in a store window. The store owner decides to choose three NHL and two CFL jerseys. These jerseys will be arranged in a row in the store window.

The number of displays that can be made by choosing the jerseys and then arranging them in the window is

A. 4900
B. 11 760
C. 117600
D. 1411 200
The answer key says the right Answer is (C), I just don't know how to get there. ​

Answers

Answer:

possible arrangements

CCNNN

CNCNN

CNNCN

CNNNC

NCCNN

NCNCN

NCNNC

NNCCN

NNCNC

NNNCC

Ten ways to arrange the window

for any one of these there are

NHL

7 ways to fill the first position

6 ways to fill the second

5 ways to fill the third

7•6•5 = 210 ways to select the NHL jerseys

CFL

8 ways to fill the first position

7 ways to fill the second

8•7 = 56 ways to select the CFL jerseys

210•56 = 11760 ways to select a set of 5 jerseys

11760•10 = 117 600 possible ways to arrange the window

Hope everyone has a happy holiday for whatever you celebrate :)

Answers

Answer:

Happy holidays to everyone!

Step-by-step explanation:

Anita plans to give her husband 3 shirts for his birthday. She narrows the search to 3 shirts from a selection of 17 shirts at Dillon's Store or 3 from a selection of 20 shirts at The Men's Shop. In how many ways can she select the shirts

Answers

Using the combination formula, it is found that she can select the shirts in 775,200 ways.

The order in which the shirt are chosen is not important, hence, the combination formula is used to solve this question.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem:

3 shirts from a set of 17.Then, 3 shirts from a set of 20.They are independent, hence, to find the total, we multiply both combinations.

[tex]T = C_{17,3} \times C_{20,3} = \frac{17!}{3!14!} \times \frac{20!}{3!17!} = 680 \times 1140 = 775200[/tex]

She can select the shirts in 775,200 ways.

To learn more about the combination formula, you can check https://brainly.com/question/25821700

Please help me!!!!!!!!!

Answers

Answer:

y=25x+1150

Step-by-step explanation:

1425-1275=150

150/6=25 so 25 dollars per month

1275-5(25)

1275-125=1150

y=25x+1150

The vertice of triangle ABC are A(8,4), B(6,3) and C(5-5). Find the angle between the side AB and BC.​

Answers

Answer:

Step-by-step explanation:

Use law of cosines

c² = a² + b² - 2abcosθ

cosθ = (c² - a² - b²) / -2ab

c = length of AC = √(8 - 5)² + (4 - (-5))² = √90

b = length of AB = √(8 - 6)² + (4 - 3)² = √5

a = length of BC = √(6 - 5)² + (3 - (-5))² = √65

cosθ = (√90² - √65² - √5²) / -2√65√5

cosθ = 20 / -36.05551...

cosθ = - 0.5547001

θ = 123.69°

Equivalent ratios
6:3 X:12 18:x

Answers

Answer: 24:12 and 18:9

Explanation: divide the number you get (e.g.12) into the number on the same side of the other ratio (e.g. 3). So, 12 divided by 3=4, so you multiply 6x3 to get 24 (24:12). Then, 18 divided by 6= 3, so 3x3= 9 (18:9)

-4(-2u+3)-u=3(u-7)-5
where you simplify your answer as much as possible ​

Answers

Answer:

-7/2

Step-by-step explanation:

-4(-2u+3)-u=3(u-7)-5

8u-12-u=3u-21-5

8u-u-12=3u-26

7u-12=3u-26

7u-3u-12=-26

4u-12=-26

4u=-26+12

4u=-14

u=-14/4

simplify

u=-7/2

Answer:

u = - 3.5

Step-by-step explanation:

Before solving this you have to know that,

(-) × (-) = (+)

(-) × (+) = (-)

(+) × (+) = (+)

Let us solve now.

[tex]-4(-2u+3)-u=3(u-7)-5[/tex]

[tex]8u-12-u=3u-21-5[/tex]

[tex]7u-12=3u-26[/tex]

[tex]7u-3u=12-26[/tex]

[tex]4u=-14[/tex]

[tex]\frac{4u}{4} = \frac{-14}{4}[/tex]

[tex]u=-3.5[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

The average price of an item is $42 with a standard deviation of $3
Find a 98% confidence interval about the mean (one decimal place).
Is a value of X=48 unusually high or is it normal? Choose correct explanation!

Answers

The mean price goes between $ 41.16 and $ 42.84, so a value of $ 48 is unusually high.

Since the average price of an item is $ 42 with a standard deviation of $ 3, to find a 98% confidence interval about the mean, and determine if a value of X = 48 is unusually high or if it is normal, the following calculations should be done:

(((42 - 3) + (42 + 3)) / 2) x 0.98 = X ((39 + 45) / 2) x 0.98 = X 42 x 0.98 = X 41.16 = X

(((42 - 3) + (42 + 3)) / 2) x 1.02 = X ((39 + 45) / 2) x 1.02 = X 42 x 1.02 = X 42.84 = X

Therefore, as the mean price goes between $ 41.16 and $ 42.84, a value of $ 48 is unusually high.

Learn more about maths in https://brainly.com/question/25908442

Mr. Irwin Sold adult tickets

Answers

Answer:

i dont know how to do it231

Step-by-step explanation:

1123234

I NEED HELP WITH #5 and #4

What is the value of f(x) = -3-x when x = -7?
A-10
) B -4
4
D 10

Answers

Answer:

#5. C 4

#4. J 0.3 meters

Step-by-step explanation:

No. 5

f(-7) = -3-(-7)

f(-7) = 4

C

No. 4

s = sqrt(0.09)

s = 0.3 meters

Zanele Situ is a disabled Olympic gold-medallist javelin champion. She threw the javelin a distance of 16,22 m in London at 2012 Olympics. She threw the javelin to a distance of 17,90 m in Rio at 2016 Olympics. By what percentage did the distance increase?​

Answers

Answer:

  10,4%

Step-by-step explanation:

The percentage change is found from ...

  (amount of change)/(original amount) × 100%

  (17,90 -16,22)/(16,22) × 100% = 1,68/16,22 × 100% ≈ 10,358% ≈ 10,4%

3,311L how many millilters

Answers

Answer:

3311 mililiters

Step-by-step explanation:

1 L = 1 liter = 1000 mililiters

3.311L = 3.311 liters = 3.311*1000 = 3311 mililiters

What is the range of the following function, if the domain is {1,3,12}?
f(x) = x - 3

Answers

I think this is the answer ( −∞,∞)

How can a person best reduce the risk of sustaining permanent injuries?

Wear protective clothing while sleeping at home.
Secure a seat belt only when riding in the front seat.
Wear a cracked bicycle helmet while riding a bicycle.
Put away guns in a lockbox that is secure and in a discrete location.

Answers

Answer:

Put away guns in a lockbox that is secure and in a discrete location.

Have a good day <3

Gravity is a force that acts upon a ball after it is thrown?


A. True


B. False

Answers

True or false, depending on the specifics. True, because the gravity makes it go to the ground. False, because gravity is always working, so you don't need to throw the ball. However since it doesn't say that it only happens when you throw it. The answer should be true.

Choose the number that makes the statement true: -5>?
a. 9
b. -9
C. -3
d. 3

Answers

Answer: This is B.) -9

Step-by-step explanation:

Step-by-step explanation:

All of those numbers are greater than -5 except for B.

48a^21 b^5
——————-
16a^21 b^4

Answers

Answer:

3b

Step-by-step explanation:

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )

Answers

Answer:

x=9

Step-by-step explanation:

since the triangles are similar, the sides are all in proportion. This means that:

[tex] \frac{uw}{eg} = \frac{uv}{fg} [/tex]

Now we can just sub in the sides:

[tex] \frac{91}{13} = \frac{56}{x - 1} [/tex]

simplify the first fraction

[tex] \frac{7}{1} = \frac{56}{x - 1} [/tex]

Now we can cross multiply

56=7(x-1)

56=7x-7

63=7x

Therefore:

×=9

CAN YOU GUYS HELP PLEASE, I HAVE A LIMIT ON THIS!!!!

Answers

Answer:

the 2nd choice

Step-by-step explanation:

hope this helps

may i get braineist pls

Answer:

A. or y=-1/3x-3

Step-by-step explanation:

PLEASE HELP!!!
List 5 fractions that are equal to 3/4!

Answers

6/8, 9/12, 12/16, 15/20, and 18/24

Answer:

9/12

6/8

30/40

27/36

15/20

Step-by-step explanation:

Solve the system of two linear equations below graphically y= -x + 1 y= -1/3+ 3

Answers

Answer:

Step-by-step explanation:

a prisms base has a perimeter of 12cm and a height of 2 cm. the area of the base was 5cm. what is the surface area of the prism.

Answers

[tex]\text{Surface Area of Prism} = (2 \times \text{Base Area}) + (\text{Base perimeter} \times \text{height})\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=(2 \times 5)+(12\times 2)\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=10+24\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=34~~ \text{cm}^2[/tex]

Other Questions
GIVING BRAINLIEST!! FAST- Which cellular process would be affected first if the structure labeled 3 weredestroyed? What challenge did stormy the brave face and how was he a hero stormieand the octopus QuestionWater is added or drained from a tank each day. The first day, 910 of a gallon is added to the empty tank. The second day, 710 of a gallon is drained from the tank. The third day, 810 of a gallon is added to the tank. The fourth day, 610 of a gallon is drained from the tank. The amount of water in the tank after 15 days is given by910+(710)+810+(610)++310+(110)+210.How much water is in the tank after 15 days? Write your answer as a decimal. What is the value of 8.25p + 3.99c, when p=11 and c= 7? * can someone please help me on this all u have to do is search up on the internet and then write 4 facts that are mentioned in the web site and give the main idea to but make sure I know were the main idea isplease help Im begging you and if u cant help then please dont Answer this is the web site (5 reasons to bring back extinct animals) Is 1/-4 the same as -1/-4 Os empreendedores so fundamentais na sociedade, pois a frente de pequenas, mdias e grandes empresas esses lderes contribuem diretamente para o crescimento da economia do pas, para a promoo de emprego e especialmente para a melhor distribuio da renda. Quando h um cenrio propenso, os empreendedores conseguem desenvolver seus empreendimentos e alavancar os resultados de seu negcio continuamente. Quando no h, isso no problema, eles fazem deste desafio uma oportunidade de ir alm e buscam nas adversidades chances reais de atender determinados nichos, capitalizar sua empresa e realizar seus sonhos. Esta a grande mentalidade empreendedora na sociedade: fazer acontecer, mostrar sua ousadia, enfrentar as dificuldades com resilincia, ser criativo, inovador para saber transformar suas oportunidades em grandes triunfos. Marques, j. R. O papel do empreendedor na sociedade. Maio/2016. Disponvel em https://www. Jrmcoaching. Com. Br/blog/o-papel-do-empreendedor-na-sociedade/ acesso em 13/06/2019 (adaptado). A mentalidade empreendedora est associada a avaliao da pessoa quanto ao ambiente em que est inserida e s condies que influenciam a deciso de empreender, quais sejam:. Which statement describes one feature of Rutherford model of the atom QUESTION 8Which of the following is NOT a factor of successful protests?O A. PacificismO B. Non-violent disruptionO C. Broad coalitionO D. Split within the elite why does not congress not rely on declarations of war Which choice is equivalent to the product below?V8,5O A. 4/10O B. 10-12C. 13O D. 22/10 Which of the following best describes how the amount of DNA in the cell changes during M phase?The amount of D N A doubles as the D N A is replicated.The amount of D N A slightly increases as a result of new organelle synthesis.The amount of D N A does not change while the cell grows.The amount of DNA is halved as the cell divides into two daughter cells. What functional group is found on the head end of a lipid molecule?a. carboxyl groupb. amino groupX c.omega-3 fatty acidd. glycerol any system of government in which rule is by the people is called What is colonization and how is what we eat in the United States connected to the historical legacy of colonization? _265Hs--->_16O+_9Be=_____? How do I solve for x? Can someone help me with this problem please! 2) 4x - 4y = -12 x + 4y = -18Solve by elimination