There are 6 people in Jacob’s family. Jacob’s sister is 5 years younger than he is. He has twin brothers who are 3 years older than he is. His mom is 3 times Jacob’s age, and his dad is 4 years older than his mom. The total of all the ages of all his family members is 165 years. How old is Jacob? Define a variable, write an equation, and solve the problem.

Answers

Answer 1

Answer:

Jacob is [tex]16[/tex] years old.

Step-by-step explanation:

Let the age of Jacob be [tex]x[/tex] years.

Jacob’s sister is [tex]5[/tex] years younger than he is.

So, the age of Jacob's sister be [tex]x-5[/tex] years.

Jacob's twin brothers are [tex]3[/tex] years older than he is.

So, the age of each of the twin brother be [tex]x+3[/tex] years.

Jacob's mom is [tex]3[/tex] times his age.

So, the age of Jacob's mom be [tex]3x[/tex] years.

Jacob's dad is [tex]4[/tex] years older than his mom.

So, the age of Jacob's dad be [tex]3x+4[/tex] years.

Now, the total of all the ages of all his family members is [tex]165[/tex] years.

So, [tex]x+x-5+x+3+x+3+3x+3x+4=165[/tex]

[tex]\Rightarrow 10x+5=165[/tex]

[tex]\Rightarrow 10x=165-5[/tex]

[tex]\Rightarrow 10x=160[/tex]

[tex]\Rightarrow x=\frac{160}{10}[/tex]

[tex]\Rightarrow x=16[/tex]

Hence, Jacob is [tex]16[/tex] years old.


Related Questions

Tabitha is 8 years younger than 4 times pats age. Tabitha is 40. How old is Pat

Answers

Answer:

pat is 62

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

point=
slope=
point slope equation=

Answers

Answer:

Point will be 1,025 after 4 years

slope is 45

equation would be y=45x+1025

Step-by-step explanation:

this is just a guess. You are free to modify it to what you think is correct

Please help will give 20 points

Answers

Answer:

not sure but i think its B

which statement best describes the graphs of the lines
A. they are parallel
B. they are the same line
C. they intersect at exactly one point
D. they intersect at exactly two points

Answers

Answer:

A

Step-by-step explanation:

Since they have the same slope and have different y-intercept they're parallel

If a circle has a diameter of 24 inches, which expression gives its area in
square inches?

A. 12^2 • pi
B. 12 • pi
C. 24 • pi
D. 24^2 • pi

Answers

A= pi x r^2

radius is diameter / 2
r= 12
so your answer is
A=pi(12)^2

(Will give brainliest) In your own words, say what a rational number is. Give at least three different examples of rational numbers.

In your own words, say what an irrational number is. Give at least two examples.

Answers

Hey there!

A rational number is a number that CAN be turned in to a fraction, like 0.5, or 9, 0r -[tex]3^2[/tex].

A rational number is a number that CANNOT be turned into a fraction, like pi, or √2.

Hope it helps and have a great dayyyyy!!!!!

pls i need help with the attachment its my hw

Answers

Answer:

C

Step-by-step explanation:

It has to be c by process of elimination the circle has to be filled in and on the #5 and as you can see the only one was C

Answer:

D

Step-by-step explanation:

Solving the inequality

2x + 3 ≤ 5 ( subtract 3 from both sides )

2x ≤ 2 ( divide both sides by 2 )

x ≤ 1

The required number line will have a solid circle at x = 1 and the arrow will be going left.

The only graph with these conditions is D

Karen has a bag containing the following marbles:
3 red marbles
4 green marbles
1 yellow marble
What is the probability of randomly selecting a
green marble or a red marble from the bag?
A. 2/3
B. 7/8
C. 3/8
D 4/5

Answers

B. 7/8 because there is 4 green and 3 red and when added up they are 7 which leaves only the yellow which is one out of the probability.

Answer:

its B because 4+3=7 and 3+4+1=8

Step-by-step explanation:

because 4+3=7 and 3+4+1=8 so it is 7/8

Find the value of x.
102
146
120
124
x
158
X

Answers

Answer:

x = 70

Step-by-step explanation:

180* (n-2)

180*(6-2)

180*(4) = 720

102 + 146 + 120 + 124 + 158 = 650

720 - 650 = 70

A polygon is a planar figure characterized by a limited number of straight-line segments. The value of the x is 70°.

What is a polygon?

A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The sum of the interior angles of a n-sided polygon is calculated using the formula,

Sum of the interior angles = (n-2) × 180°

For the given polygon, the number of sides is equal to 6. Therefore, the sum of the interior angles of the polygon is,

Sum of the interior angles = (6-2) × 180°

                                            = 4 × 180°

                                            = 720°

Further, the sum of the interior angles for the given polygon can be written as,

Sum of the interior angles = 102° + 146° + 120° + 124° + 158° + x°

720° = 102° + 146° + 120° + 124° + 158° + x°

x = 720° -  (102° + 146° + 120° + 124° + 158°)

x = 720° - 650°

x = 70°

Hence, the value of the x is 70°.

Learn more about Polygon here:

https://brainly.com/question/10441863

#SPJ2

Solve for x.

PLease need help

Answers

Answer:

x=7

Step-by-step explanation:

22x-4=7x-4+105

cancel both 4 out

22x=7x+105

15x=105

x=7

Carrie got a $65 gift certificate. She plans to buy a $12 rose bush and as many seed packets as she can for $1.79 each. Which of these inequalities shows x, the number of seed packets she can buy?

Answers

Answer:

she can buy the rose bush and 29 packets of seeds. So i think X= 29

Step-by-step explanation:

Sales Tax
Selling Price Rate of Sales Tax Sales Tax
$40.00
6%
?

Answers

Answer:

The sales tax is 2.40 so I hope that helps u

Answer:

2.40

Step-by-step explanation:

price x sales tax rate = sales tax

40 x .06(6%)=sales tax

2.40=sales tax

find the equation of the axis of symmetry and the coordinates of the vertex of the graph of each function.​

Answers

Answer:

Axis of symmetry is 0

vertex is 1

Step-by-step explanation:

x^2+19=10 solve algebraically
4x^2+3=43 solve algebraically

Answers

Answer:

[tex]a)\ x_1=-3i,\ x_2 =3i[/tex]

[tex]b)\ x_1=-\sqrt{10},\ x_2=\sqrt{10}[/tex]

Step-by-step explanation:

Given equations:

[tex]a)\ x^2+19=10\\\\b)\ 4x^2+3=43[/tex]

A. x² + 19 = 10

Step 1: Subtract 19 from both sides.

[tex]\\\implies x^2+19-19=10-19\\\\\implies x^2=-9[/tex]

Imaginary number rule: For any positive real number "k", [tex]\sqrt{-k} = i\sqrt{k}[/tex]

Note: Two imaginary (complex) solutions indicate that the graph will not intersect the x-axis. As a result, it has no real roots.

Step 2: Take the square root of both sides (positive and negative roots).

[tex]\\\implies \sqrt{x^2}=\sqrt{-9}\\\\\implies x=\pm\ i\sqrt{9}\\\\\implies x=\pm\ 3i[/tex]

Step 3: Separate the solutions.

[tex]\implies x_1=-3i,\ x_2 =3i[/tex]

----------------------------------------------------------------------------------------------------------------

B. 4x² + 3 = 43

Step 1: Subtract 43 from both sides.

[tex]\\\implies 4x^2++3-3=43-3\\\\\implies 4x^2=40[/tex]

Step 2: Divide both sides by 4.

[tex]\\\implies 4x^2=40\\\\\implies \dfrac{4x^2}4=\dfrac{40}{4}\\\\\implies x^2=10[/tex]

Step 3: Take the square root of both sides (positive and negative roots).

[tex]\\\implies \sqrt{x^2}=\sqrt{10}\\\\\implies x=\pm\ \sqrt{10}[/tex]

Step 4: Separate the solutions.

[tex]\implies x_1=-\sqrt{10},\ x_2=\sqrt{10}[/tex]

7. A rectangle has a perimeter of 24 motors
and an area of 35 square meters, what is
the length in meters of the longer side?
AI
B. 3
c.5
D.7
E8

Answers

Answer:

D

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

D

why must it be more than 20 characters???

find the inverse equation
f(x) = 2x – 3

Answers

I will help but, what is x supposed to be?

A cyclist travels 15 miles in 45 minutes.
What is his average speed in mph?

Answers

The cyclist’s average speed in mph is 20mph

The answer is 20 Km/hr

first : you have miles . then change it into Km .

second: 45 min to sec

finally speed is the distance per unit time

Help me please with math

Answers

Answer:

B. 1 and 10

Step-by-step explanation:

answer is b....have a good day

Use the Distributive Property and write the sum of the number as the product of the GCF.
30 + 12

Answers

Answer:

1,2,3 and 6 is the answer

3-2(3x+1)=19
How would I solve this equation?​

Answers

Step-by-step explanation:

3-2(3x+1)=19

[tex]3 - 6x - 2 = 19 \\ 1 - 6x = 19 \\ - 6x = 19 - 1 \\ - 6x = 18 \\ x = - 3[/tex]

SOLUTION
5 Salvador drives 6.5 miles to his aunt's house. For every mile Salvador drives, the
amount of gas in the car's gas tank changes by -0.04 gallon. What is the total
change in the gallons of gas in the car's tank? Show your work.
SOLUTION

Answers

Answer:

-0.26 gallon

Step-by-step explanation:

-0.04x 6.5=0.26

Which pairs of polygons are congruent?

Answers

Answer: Pair 1 and Pair 4

Step-by-step explanation:

Pair 1 and pair 3

The two polygons in pair 2's perimeter aren't the same, thus they aren't congruent with each other, the same goes for pair 4

Write an exponential function in the form y=ab^x that goes through points (0,9) and (3, 576)

Answers

Answer:

An exponential function in the form y=9(4ˣ)

Step-by-step explanation:

Step(i):-

Given that exponential function

                  y = a bˣ ...(i)

The equation (i) passes through the point (0,9)

               9 = a (b )⁰ = a

             a =9

Step(ii):-

The equation (i) passes through the point (3,576)

            576 = 9(b)³

         ⇒    [tex]\frac{576}{9} = b^{3}[/tex]

      ⇒     64 = b³

     ⇒     4³ = b³

             [tex](4^{3} )^{\frac{1}{3} } = (b^{3} )^{\frac{1}{3} }[/tex]

             b = 4

Final answer:-

An exponential function in the form y=abˣ

An exponential function in the form y=9(4ˣ)

 


The quotient x divide 5 is a negative integer. Name two
integers that x could represent and find the quotients

Answers

Answer:

Herk in a boo

Step-by-step explanation:

Elimination method 3x + y = 14 4x - y = 7

Answers

Answer:

(3,5)

x=2 and y=5

Do 4x and 15+x have the same value when x is 5?
Are 4x and 15+x equivalent expressions? Explain your reasoning.

Answers

Answer:

1. yes 2. no

Step-by-step explanation:

Hi there!

When x is equal to 5, 4x and 15+x have the same value because 4*5= 20 and 15+5 = 20.

4x and 15+x are not equivalent expressions because they cannot be simplified to create the same expression nor will they produce the same answer every time.

I hope this helps!

Find the quotient 7/9 divide 5/6

Answers

Answer:

7/9 ÷ 5/6 = 42/45 as simplified as 14/15 in fraction form. 7/9 ÷ 5/6 = 0.9333 in decimal form.

Step-by-step explanation:

Answer:

14/15

Step-by-step explanation:

7/9 x 6/5 = 42/45 = 14/15

brainliest pls

plz answer for 35 points​

Answers

The answer is b I think hope this helps

Answer:

The answer is B.

Step-by-step explanation:

Two lighthouses flash their lights every 20 seconds and 30 seconds respectively. Given that they flash together at 8 p.m, when will they next flash together?

Answers

One minute later at 8:01pm. One lighthouse will flash 3 times (at 20, 40 and 60 seconds)...the other will flash twice (at 30 and 60 seconds). So they will both flash 60 seconds later, at 8:01

Please help me thankss

Answers

Answer:

1/2

Step-by-step explanation:

you can find the ratio by doing 12 / 6 and you will get 2 then you dump a 1 over the 2 to get 1/2 that's not how it works in all tho

Answer:

1:1

Step-by-step explanation:

if the rule was 1:2 then they would have won 4 games so its 1:1

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