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
Eddi Din [679]
3 years ago
10

ou find 38 coins consisting only of nickels, dimes, and quarters, with a face value of $4.75. However, the coins all date from 1

926, and are worth considerably more than their face value. A coin dealer offers you $8 for each nickel, $6 for each dime, and $22 for each quarter, for a total of $410. How many dimes did you find? Type in your numerical answer only; do not type any words or letters with your answer.
Mathematics
1 answer:
Dmitrij [34]3 years ago
8 0

Answer:

17

Step-by-step explanation:

First of all let us assume the following:

Let the number of nickels = n

Let the number of dimes = d

Let the number of quarters = q

Note also the following conversion factors:

1 nickel = $0.05

1 dime = $0.1

1 quarter = $0.25

we are given the following information:

n + d + q = 38. . . . (1)   (38 coins consisting only of nickels, dimes, and quarters)

0.05n + 0.1d + 0.25q = 4.75 ( we can remove decimals by multiplying through by 100 to give)

5n + 10d + 25q = 475 . . . . (2) note that equation 2 can also be simplified by dividing through by 5, to give the following)

n + 2d + 5q = 95 . . . . . (2)

8n + 6d + 22q = 410 . . . . (3)

Next we will look for a way to eliminate two of the unknowns in each equation to have just one unknown that we can use to solve.

we have three equations

n + d + q = 38. . . . . . . . (1)

n + 2d + 5q = 95 . . . . . (2)

8n + 6d + 22q = 410 . . .(3)

Next we will look for a way to eliminate two of the unknowns in each equation to have just one unknown that we can use to solve.

we can eliminate n by subtracting equation (1) from (2) {eq (2) - eq (1)}

(n - n) + (2d - d) + (5q - q ) = (95 - 38)

= d + 4q = 57 . . . . . . (3)

Next we can multiply eqn (1) through by 8, to make it look like eqn (3), the we can subtract eqn (1) from eqn (3) as follows:

eqn (1) × 8 = 8 × (n + d + q = 38)

8n + 8d + 8q = 304 . . . . (1b) ; subtracting this from eqn (3) we have:

(8n - 8n) + (6d - 8d) + (22q - 8q) = (410 - 304)

= -2d + 14q = 106 . . . . (4)

Now, we have two simplified equations that we can work with:

d + 4q = 57 . . . . . . (3)

-2d + 14q = 106 . . . . (4)

from eqn (3), making 'd' the subject of the formular:

d = 57 - 4q ; replacing the value of d in eqn 4 with this value, we have:

-2(57 - 4q) + 14q = 106

-114 + 8q + 14q = 106

-114 + 22q = 106

22q = 106 + 114 = 220

22q = 220

∴ q = 220 ÷ 22 = 10

∴ q = 10

Next let us solve for 'd' by replacing the value of q with 10 in eqn (3)

d + 4q = 57 . . . . . . (3)    (but q = 10)

d + 4(10) = 57

d + 40 = 57

d = 57 - 40 = 17

d = 17

finally to solve for n, let us input the values of q and d into eqn (1)

n + d + q = 38. . . . (1)  (q = 10 ; d = 17)

n + 17 + 10 = 38

n + 27 = 38

∴ n = 38 - 27 = 11

Therefore the number of each coin are as follows:

nickel = 11

dime = 17

quarters = 10

<em>the solution is quite lengthy, but if you don't understand it at first look, please go through it again.</em>

You might be interested in
What is the sum of all the integers that have values between 42 and 87
lara31 [8.8K]

Answer:

9 and 10

Step-by-step explanation:

7 0
3 years ago
Look at the attached photo
Papessa [141]

Answer:

Step-by-step explanation:

radius of the circle=12 cm / 2=6 cm

Area of the square=side²=(12 cm)²=144 cm²

Area of the circle=πr²=(3.142)(6 cm)²≈(3.142)*36 cm²≈113.112 cm²

Area of the four  sides between the square and the circle=

=Area of the square - area of the circle=144 cm²-113.112 cm²=30.888 cm²

shaded area =30.888 cm²/4=7.722 cm²

Answer =7.722 cm²

6 0
2 years ago
4d + 5 &gt;= 13 or 7d - 2 &lt;12
vivado [14]
I'm guessing that the >= is a greater than or equal to sign, so the answer should be d>=2 and d<2, please tell me if I am wrong and I will do my best to correct it!

6 0
3 years ago
Please help me!
marusya05 [52]

Answer:


Step-by-step explanation:

Nice summary problem.

<AEC

  • AEC = 360 - 243.5 = 116.5    
  • The number of degrees in 1 rotation of a circle = 360o. You have accounted for 243.5 degrees. What is left over is the answer.

<EAD and <ECD

Both of these are tangents to a circle. Tangents meet radii at 90 degree angles.

<EAD = <ECD = 90 degrees

<ABC

<ABC is 1/2 the central angle. The Central angle is <AEC

  • < AEC = 116.5
  • <ABC = 1/2 * 116.5
  • <ABC = 58.25

<ADC

There are 2 ways of doing this. You should know both of them.

<em><u>One</u></em>

All quadrilaterals = 360 degrees. You know three of the angles. You should be able to find ADC

  • <ADC + 90 + 90 + 116.5 = 360     Add the four angles together.
  • <ADC + 296.5 = 360                   Combine terms on the left
  • <ADC = 360 - 296.5                    Subtract 238.25 from both sides
  • <ADC = 63.5                                 Answer

<em><u>Method Two</u></em>

<ADC = 1/2 (major Arc - Minor Arc)  This formula is fundamental to circle / tangent properties. The Major arc is the larger of the two parts of the circumference of a circle. The Minor arc is the smaller.

  • <ADC = 1/2(243.5 - 116.5)
  • <ADC = 1/2(127)
  • <ADC = 63.5
8 0
3 years ago
Make an equation for the line v=(6,6) is perpendicular to y=-2/3x-11
natali 33 [55]

Answer:

y=-2/3x+10

Step-by-step explanation:

y=2/3x-11

plug in plot and remove intercept

6=-2/3(6)+b

6=-4+b

10=b

y=-2/3x+10

5 0
2 years ago
Other questions:
  • Can someone check if this is right? simple probability but i am unsure if my answer
    7·1 answer
  • Dose anyone know how to solve this
    11·2 answers
  • Restating the conditions of problem 1, the cost to buy t-shirts is $5.00 for the first 10 shirts, $4.00 for each additional shir
    7·2 answers
  • Solve using the distributed property -4(2x-5)=4
    11·2 answers
  • Last year a website had 40,000 visitors and this year it had 37,000 visitors.What is the percent change in the number of visitor
    8·1 answer
  • Please help me you guys
    13·1 answer
  • You want to buy a tent in the shape of a pyramid. The rectangular base is 35 square feet, with a height of 4 feet. What is the v
    14·1 answer
  • How long will it take you to ski at a distance of 36 miles at the speed of 3 mph
    12·2 answers
  • 1. K + 8 &gt; 19, if k = 11 is this a true statement
    8·1 answer
  • Let R(x)=3x3+2x2+x and S(x)=4x2+1. Find R(x)+S(x).
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!