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ikadub [295]
3 years ago
13

A cashier has a total of 30 bills consisting of ones, fives and twenties. the number of twenties is 5 less than the number of on

es. the total value of money is $229. how many of each denomination of bill are there?
Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
7 0

Let us say that:

a = ones

b = fives

c = twenties

 

So that the total money is:

1 * a + 5 * b + 20 * c = 229

=> a + 5b + 20c = 229                                       --> eqtn 1

 

We are also given that:

c = a – 5                                                                --> eqtn 2

a + b + c = 30                                                      --> eqtn 3

 

Rewriting eqtn 3 in terms of b:

b = 30 – a – c

Plugging in eqtn 2 into this:

b = 30 – a – (a – 5)

b = 35 – 2a                                                           --> eqtn 4

 

Plugging in eqtn 2 and 4 into eqtn 1:

a + 5(35 – 2a) + 20(a – 5) = 229

a + 175 – 10a + 20a – 100 = 229

11a = 154

a = 14

 

So,

b = 35 – 2a = 7

c = a – 5 = 9

 

Therefore there are 14 ones, 7 fives, and 9 twenties.

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PIT_PIT [208]

The solution to the equation is p = 1/3 and q = undefined

<h3>How to solve the equation?</h3>

The equation is given as:

p^2 - 2qp + 1/q = (p - 1/3)

The best way to solve the above equation is by the use of a graphing calculator i.e. graphically

However, it can be solved algebraically too (to some extent)

Recall that the equation is given as:

p^2 - 2qp + 1/q = (p - 1/3)

Split the equation

So, we have

p^2 - 2qp + 1/q = 0

p - 1/3 = 0

Solve for p in p - 1/3 = 0

p = 1/3

Substitute p = 1/3  in p^2 - 2qp + 1/q = 0

So, we have

(1/3)^2 - 2q(1/3) + 1/q = 0

This gives

1/9 - 2/3q + 1/q = 0

This gives

2/3q + 1/q = -1/9

Multiply though by q

So, we have

2/3q^2 + 1 = -1/9q

Multiply through by 9

6q^2 + 9 = -q

So, we have

6q^2 + q + 9 = 0

Using the graphing calculator, we have

q = undefined

Hence. the solution to the equation is p = 1/3 and q = undefined

Read more about equations at:

brainly.com/question/13763238

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5 0
2 years ago
1. What is the solution to 5 + t = 23 a. T=28 b. T=18 c. T= -18 d. T= -23 2. What is the value of b if -7 + b = -8 a. B=15 c. B=
kramer
The answer to number one is 18 and the answer to number two is -1
3 0
3 years ago
Read 2 more answers
I need help fast pleasee
trapecia [35]

Answer:

<em>y = - cos ( </em>\frac{3}{4}<em> x + </em>\frac{\pi }{4}<em> ) </em>

Step-by-step explanation:

y = A cos ( Bx + C) + D

Vertical shift D = 0

A = - 1

Compression / Stretching B

Period of given function is \frac{8\pi }{3}

Period of cos x is 2π

\frac{8\pi }{3} = \frac{2\pi }{B} ⇒ B = \frac{3}{4}

Horizontal shift is C ÷ B

Horizontal shift of given function is \frac{\pi }{3}

\frac{\pi }{3} = C ÷ \frac{3}{4} ⇒ C = \frac{\pi }{4}

So, the equation of given function is

<em>y = - cos ( </em>\frac{3}{4}<em> x + </em>\frac{\pi }{4}<em> ) </em>

4 0
2 years ago
State the domain of the sets of points. [-4,9] [8,9] [5,-7] [-6,1] [2,7]
Ainat [17]

Answer:

[-6, -4, 2, 5, 8]

Step-by-step explanation:

take the first number in each pair and put them in numerical order (least to greatest)

3 0
3 years ago
Write and solve a real-world problem that can be represented by the expression (-3)(5)+10.
Blizzard [7]

Hi!

(-3)(5)+10

-15+10

=-5

<u>Explanation: </u><u><em>This question is about math, and this lesson is about order of operations. I will give you a hint. You had to used PEMDAS, P-Parenthesis should be go first, E-Exponents, M-Multiply, D-Divide, A-Add, and S-Subtract. If you use multiply, divide, add, or subtract it should go left to right. First, you had to multiply and divide should go left to right. And it gave us -15+10.  And finally, you should add and subtract by left to right. And it gave us -5 is correct answer. Hope this helps! Thank you for posting your question at here on Brainly. And have a great day. -Charlie</em></u>

5 0
3 years ago
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