1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MAXImum [283]
2 years ago
8

1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the

equation?
2) A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 4 more of the twenties. The total value of the money is $305.00. Find the number of twenty-dollar bills. What is the equation?
Mathematics
1 answer:
Mice21 [21]2 years ago
5 0

Answer:

Part 1) Helen's age is 32 years old and Jane's age is 24 years old

Part 2) 13 twenty-dollar bills

Step-by-step explanation:

Part 1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the equation?

Let

x----> Helen's age

y---> Jane's age

we know that

x=y+8 ----> equation A

(x-20)=3(y-20) -----> equation B

substitute equation A in equation B and solve for y

(y+8-20)=3(y-20)

y-12=3y-60

3y-y=60-12

2y=48

y=24 years

Find the value of x

x=y+8

x=24+8=32 years

Part 2)

Let

x-----> the number of five-dollar bills

y----> the number of twenty-dollar bills

we know that

5x+20y=305 -----> equation A

y=x+4 ------> x=y-4 ------> equation B

substitute equation B in equation A and solve for y

5(y-4)+20y=305

5y-20+20y=305

25y=325

y=13 twenty-dollar bills

Find the value of x

x=y-4

x=13-4=9  five-dollar bills

You might be interested in
A statue is mounted on top of a 21 foot hill. From the base of the hill to where you are standing is 57feet and the statue subte
AleksandrR [38]

Please find the attached diagram for a better understanding of the question.

As we can see from the diagram,

RQ = 21 feet = height of the hill

PQ = 57 feet = Distance between you and the base of the hill

SR= h=height of the statue

\angle SPR=Angle subtended by the statue to where you are standing.

\angle x=\angle RPQ= which is unknown.

Let us begin solving now. The first step is to find the angle \angle x which can be found by using the following trigonometric ratio in \Delta PQR :

tan(x)=\frac{RQ}{PQ} =\frac{21}{57}

Which gives \angle x to be:

\angle x=tan^{-1}(\frac{21}{57})\approx20.22^{0}

Now, we know that\angle x and \angle SPR can be added to give us the complete angle \angle SPQ in the right triangle \Delta SPQ.

We can again use the tan trigonometric ratio in \Delta SPQ to solve for the height of the statue, h.

This can be done as:

tan(\angle SPQ)=\frac{SQ}{PQ}

tan(7.1^0+20.22^0)=\frac{SR+RQ}{PQ}

tan(27.32^0)=\frac{h+21}{57}

\therefore h+21=57tan(27.32^0)

h\approx8.45 ft

Thus, the height of the statue is approximately, 8.45 feet.

3 0
3 years ago
How to solve this <br>3 = (2x + 8)/3​
seropon [69]

Answer:

x = 1/2

Step-by-step explanation:

First you want to get rid of the fraction, so you can multiply both sides of the equation by 3.

9 = 2x + 8

Then, subtract 8 from both sides to get x by itself.

1 = 2x

Finally, divide both sides by 2 so you only have one x

1/2 = x

This means that the answer is x = 1/2.

5 0
3 years ago
Read 2 more answers
A taxi costs 1.65 for the first mile and 0.85 for each additional mile. Which equation could be solved to find the number x of a
diamong [38]
1.65 + 0.85x= $20
           0.85x=$18.35
                 x=21 10/17 
first you write the equation 
then you have to subtract 1.65 from the equation but you also have to subtract it from 20 
then you divide 0.85 from 0.85x and from the 18.35 left over from subtracting 1.65 from 20 
then you should get x=21 10/17 (simplified) but the decimal form is a ongoing fraction so you can just round it up to the nearest hundredth 
5 0
3 years ago
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
velikii [3]
This is a question that needs a bit of common sense to get to the actual answer that is desired. Firstly there is one information given .The other information has to be found from common sense. ! single handshake requires 2 people. Now we can easily determine the number of people doing 66 handshakes.
Then
The number of people required for 1 hand shake = 2
Then
The number of people required to do 66 handshakes = ( 2 * 66) people
                                                                                     = 132 people
Then it can be said that there were 132 people in the party. I hope the process of doing this problem is clear to you.
4 0
3 years ago
Read 2 more answers
Plz plz help I will get you points :---/
ladessa [460]
I would think it would be B
5 0
3 years ago
Read 2 more answers
Other questions:
  • Identify which type of sampling is used. A rescarch team wants to study the demographics of 9) college students in the U.S. usin
    5·1 answer
  • I need help with this .....
    11·1 answer
  • What is the midpoint between (-8, 5) and (2, -2)?
    12·1 answer
  • If a solid consists of three lateral faces and a base that are congruent isosceles triangles, what type of solid is it?. A. octa
    7·2 answers
  • PLEASE HELP !!!! ILL GIVE BRAINLIEST !!! 100 POINTS
    13·2 answers
  • Which rule describes the translation?
    15·1 answer
  • Is the graph below linear function or non- linear plxxx helppp<br><br>​
    7·1 answer
  • Marc runs 24 miles in 6 hours. At that rate, how many miles would he run in 4 hours?
    13·2 answers
  • Gabriella bought three melons for 7.50 how many melons can April buy if she has 17.50
    11·1 answer
  • What is the maximum value of P = 24x + 30y, given the constraints on x and y listed below?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!