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
Vlada [557]
3 years ago
12

A rich woman deposits a whole number of dollars x in her bank. The next time she deposits y dollars (still a whole number). Each

subsequent deposit is the sum of the two previous deposits. Her 5th deposit was only $90, but her 10th deposit is exactly one thousand dollars. Find x and y first, then answer the question. Show your work.
What is the total amount of money in the bank?
Mathematics
1 answer:
grin007 [14]3 years ago
5 0

Answer:

x = 12

y = 22

Total amount = $2596

Step-by-step explanation:

First let's find the value of each deposit until the 10th in relation to x and y:

1st: x

2nd: y

3rd: x + y

4th: x + 2y

5th: 2x + 3y

6th: 3x + 5y

7th: 5x + 8y

8th: 8x + 13y

9th: 13x + 21y

10th: 21x + 34y

Now, we can write a system with two equations and two variables:

2x + 3y = 90

21x + 34y = 1000

From the first equation: x = (90 - 3y)/2

Using this value of x in the second equation, we have:

21*(90 - 3y)/2 + 34y = 1000

945 - 31.5y + 34y = 1000

2.5y = 55

y = 22

Now we can find x:

x = (90 - 3*22)/2 = 12

Now, summing all the deposits, we have a total of 55x + 88y, which is equal to 55*12 + 88*22 = $2596

You might be interested in
Alexis and Tasha challenged each other to a
Anvisha [2.4K]

Answer:

45 WPM

Step-by-step explanation:

A = 1.2T

54 = 1.2T

T = 45

8 0
3 years ago
Read 2 more answers
I need help with this.
Sloan [31]

9514 1404 393

Answer:

  61.4

Step-by-step explanation:

The length of two semicircles of diameter 10 is the circumference of a circle of that diameter:

  C = πd = 10π ≈ 31.4

The perimeter includes that length plus the lengths of two straight sides that are 15 units each.

  P = 31.4 + 2×15

  P = 61.4 . . . . units

4 0
3 years ago
Draw a model to write 2 3/5 as an improper fraction
algol13
2 3/5 as improper fraction = 13/5
4 0
3 years ago
Read 2 more answers
Suppose that a and b are integers, a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ) . Find the integer c with 0 ≤ c ≤ 12 such that: c ≡ 9 a
g100num [7]

Answer:

A) For c ≡ 9 a ( mod 13 ) ; C is 10

B) For c ≡ 11 b ( mod 13 ) ; C is 8

C) For c ≡ a + b ( mod 13 ); C is 0

D) For c ≡ a² + b² ( mod 13 ); C is 6

E) For c ≡ a² − b² ( mod 13 ) ; C is 0

Step-by-step explanation:

This is a modular arithmetic problem where a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ).

And 0 ≤ c ≤ 12.

A) c ≡ 9 a ( mod 13 )

Substituting the value of a to obtain;

c ≡ 9 x4 ( mod 13 ) = 36 mod 13

To find 36 mod 13 using the Modulo Method, we first divide the Dividend (36) by the Divisor (13).

Second, we multiply the whole part of the Quotient in the previous step by the Divisor (13).

Then finally, we subtract the answer in the second step from the Dividend (36) to get the answer. Here is the math to illustrate how to get 36 mod 13 using Modulo Method:

36 / 13 = 2.769231

2 x 13 = 26

36 - 26 = 10

Thus, the answer to "What is 36 mod 13?" is 10

So C = 10

B) c ≡ 11 b ( mod 13 ) = 11 x 9 ( mod 13 ) = 99 ( mod 13 )

Using the same method as above,

99 ( mod 13 );

99 / 13 = 7.6155

7 x 13 = 91

99 - 91 = 8

So, C = 8

C)c ≡ a + b ( mod 13 ) = 4 + 9 (mod 13) = 13 (mod 13)

Thus;

13 / 13 = 1

1 x 13 = 13

13 - 13 = 0

So, C = 0

D)c ≡ a² + b² ( mod 13 ) = 4² + 9²( mod 13 ) = 16 + 81 ( mod 13 ) = 97 ( mod 13 )

Thus;

97 / 13 = 7.46154

7 x 13 = 91

97 - 91 = 6

So, C = 6

E)c ≡ a² − b² ( mod 13 )= 4² - 9²( mod 13 ) = 16 - 81 ( mod 13 ) = - 65 ( mod 13 )

Thus;

-65 / 13 = - 5

-5 x 13 = - 65

-65 - (-65) = 0

So, C = 0

3 0
3 years ago
A specialty shop procures silver necklaces for 15$ a piece and offers them to customers for 33$ each. What is the mark-up percen
lidiya [134]

Answer:

54.5%

Step-by-step explanation:

Given data

Cost price= $15

Selling price= $33

Mark up percent =????

%markup= selling-cost/selling*100

substitute

%markup= 33-15/33*100

%markup= 18/33*100

%markup=0.545*100

%markup= 54.5%

Hence the Percent markup is 54.5%

6 0
2 years ago
Other questions:
  • A rectangular yard measuring 26ft by 40ft is bordered (and surrounded) by a fence. Inside, a walk that is 2ft wide goes all the
    13·1 answer
  • Write the inequality represents the verbal expression-<br> All real numbers less than 69
    10·1 answer
  • Solve.
    12·2 answers
  • Help me with my question please!!❤️
    9·1 answer
  • How do you find lateral surface area​
    15·1 answer
  • Pls answer I mark brainliest
    15·1 answer
  • AHH I SHALL GIVE U POINTS FOR THIS CAUSE I AM LAZY AND DON'T WANNA DO IT ON MY OWN
    8·2 answers
  • footpath is to be constructed in a park in the shape of a parallelogram. When a coordinate plane is laid over a map of the park,
    6·1 answer
  • Langston estimated the temperature to be 45°F . The thermometer showed the actual temperature to be 50°F. Complete the steps bel
    11·1 answer
  • 20. In the figure at right, ABDC lies in plane k and AD IDC.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!