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
yarga [219]
3 years ago
12

A cash box contains $74 made up of quarters, half-dollars, and one-dollar

Mathematics
1 answer:
Strike441 [17]3 years ago
6 0

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

0.25q+0.50h+1.00d=74

\displaystyle{h=\frac{3}{5}d+1}

q=4(d+h)

Then, substitute <em>q</em> in the first equation with the expression from the third equation:

0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74

Next, substitute <em>h</em> in that equation with the expression from the second equation:

\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}

2d+0.9d+1.5=74\\2.9d+1.5=74

Solve for <em>d</em>, the number of one-dollar coins:

2.9d+1.5=74\\2.9d=72.5\\d=25

Substitute 25 for <em>d</em> in the second equation to find <em>h</em>, the number of half-dollar coins:

\displaystyle{h=\frac{3}{5}d+1}

\displaystyle{h=\frac{3}{5}(25)+1}

h=15+1\\h=16

Substitute 25 for <em>d</em> and 16 for <em>h</em> in the third equation to find <em>q</em>, the number of quarters:

q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164

Then, verify that the coins total $74:

0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

\displaystyle{h=\frac{3}{5}d+1}

\displaystyle{16=\frac{3}{5}(25)+1}

16 = 15 + 1\\16 = 16\\\text{Check.}

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}

You might be interested in
Una empresa fabrica dos productos, X y Y. Cada cantidad del articulo X producida requiere dos horas de trabajo en una taladrador
Zarrin [17]

Answer:

la respuesta esta abajo

Step-by-step explanation:

a) Sea x el número del artículo x mientras que y representa el número del artículo y.

Dado que cada cantidad de artículo x requiere 2 horas de trabajo de perforación, mientras que cada cantidad de artículo y requiere 5 horas de trabajo de perforación. Hay un máximo de 40 horas disponibles, por tanto el modelo se da como:

2x + 5y ≤ 40

b) La trama se trazó utilizando la herramienta gráfica en línea de geogebra.

c) Para 10 unidades de X y 5 unidades de y:

2 (10) + 5 (5) = 45> 40

Por lo tanto, esto no sería posible porque requerirá 45 horas de perforación, lo que es más que el máximo de 40 horas disponibles.

8 0
3 years ago
Find all values of x in the interval [0, 2π] that satisfy the equation. <br><br>6sin²(x) = 3
34kurt

Answer:

The solutions are π/4, 3π/4,5π/4,7π/4

Step-by-step explanation:

The given equation is

6sin²(x) = 3

Divide by 6 to get:

{ \sin}^{2} (x) =  \frac{1}{2}

This implies that;

\sin(x) = \pm  \frac{ \sqrt{2} }{2}

If

\sin(x) = \frac{ \sqrt{2} }{2}

x =  \frac{\pi}{4}

in the first quadrant

x =  \frac{3\pi}{4}

in the second quadrant.

If

\sin(x) = -  \frac{ \sqrt{2} }{2}

x =  \frac{5\pi}{4}

in the third quadrant

x =  \frac{7\pi}{4}

5 0
3 years ago
Does someone get this?
Anna11 [10]

Answer:

C.

Explication:

It wants you to determined which angle is bigger out of two of the angles.

Angle A. is 3.9 inches plus 7.9 inches

Angle B. is 3.9 inches plus 4.2 inches

Angle C. is 7.9 inches plus 4.2 inches

4 0
3 years ago
Read 2 more answers
The cell phone company decided to collect similar data but this time they collected information of texting speed according to ag
Ludmilka [50]

Step-by-step explanation:

As we know, Scatter plots resembles line graphs in that they are plotted on the x and y axis and the purpose of a scatter plot is to shows if the variables are related to each other. If yes, they can draw a line of best fit which can expose or go through most of the points in the plot.

Given the information in the question, we know:

"they collected information of texting speed according to age"

=> We have 2 variables here which are age and (texting speed)

Step 1:

  • Label the x-axis the input variable (age)
  • Label the y-axis the output variable (texting speed)

Step 2: Plot the points according to age and texting speed

Hence, from that plot, it could have two cases in the relation of age and texting speed which are "the more time, more text is written", or "the less time, more text is written".

7 0
3 years ago
Read 2 more answers
Multiply the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending pow
attashe74 [19]
32x^2+64x+12x+21 => 32x^2+76x+21 you multiply the two equation together and you will get this
4 0
3 years ago
Other questions:
  • WILL MARK BRAINLY IF CORRECT!
    8·1 answer
  • Identify any solutions to the system given below.<br> 2x + y = 5<br> 3y = 15 - 6x
    11·1 answer
  • Harry church borrowed 17,500.00 at 6.5% exact interest. He had to pay back a maturity value of 17,873.97 to pay off the loan. Wh
    6·1 answer
  • What is a equation in slope intercept form for the line that has a slope -1 that passes through (-4,3)
    7·2 answers
  • -5(4-2j) in its simpilest form
    6·1 answer
  • Ramona says the factor game might also be called the divisor game. Do you agree? Why or why not?
    10·1 answer
  • Simplify the expression:<br> 3(x+2) - 4 - 7x
    12·1 answer
  • Calculate the speed for a car that went a distance of 125 miles in
    9·1 answer
  • PLEASE HELP!! What is the standard deviation of a data set whose values are all the same?
    13·2 answers
  • Complete the sentence.<br> 4ft= ____ in.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!