A bank contains 30 coins, consisting of nickels, dimes, and quarters. There are twice as many nickels as quarters and the remaining coins are dimes. If the total value of the coins is 3.35. What is the number of each type of coin in the bank?
Answers
Answer:
Quarters: 7
Dimes: 9
Nickels: 14
Step-by-step explanation:
Bank --> 30 coins
Base Equations:
N+D+Q=30
5N+10D+25Q=335
Equation 1: 2Q=N
Equation 2: D=30-(N+Q)
Substitute Equation1 : D=30-(2Q+Q)
D=30-3Q
0.05(2Q)+0.10(30-3Q)+0.25Q=3.35
0.10Q+3-0.3Q+0.25Q=3.35
0.5Q+3=3.35
0.5Q=0.35
Q=7
if Q=7, N= 2*Q
N=14
D=9
Check Step:
7*25=175
14*5=70
9*10=90
175+70+90=335
Correct
Final answer:
To solve the problem, equations based on the relations between the number of nickels, dimes, and quarters are established. By substituting into these equations and solving them, it was determined that the bank contains 10 quarters, 20 nickels, and 0 dimes.
Explanation:
The student's question relates to solving a system of equations based on the given conditions regarding nickels, dimes, and quarters in a bank. Let's denote the number of quarters as q, the number of nickels as n, and the number of dimes as d. According to the problem, there are twice as many nickels as quarters, so we can write n = 2q. The total number of coins is 30, which gives us the equation n + d + q = 30. The total value of the coins is $3.35, which translates to 0.05n + 0.10d + 0.25q = 3.35. Using these three equations, we can solve for n, d, and q.
- First equation (number of nickels and quarters): n = 2q
- Second equation (total number of coins): n + d + q = 30
- Third equation (total value of coins): 0.05n + 0.10d + 0.25q = 3.35
Substituting the first equation into the other two, and solving for q and d, we find that there are 10 quarters, 20 nickels, and 0 dimes. Thus, in the bank there are 10 quarters, 20 nickels, and no dimes.
Learn more about System of Equations here:
#SPJ3
Related Questions
What is the answer to this equation 13-3/2x=34
ERROR ANALYSIS Describe and correct the error in finding the x-intercept.-2x + 3y = 12-2(0) + 3y = 123y = 12y=4
2/5m-4+ is what =16+what
What is a rational number between 1/8 and 1/4?
113 square centimeters
126 square centimeters
327 square centimeters
Answers
SA = pi * r * l + pi * r^2
where SA stands for surface area, r stands for radius, and l stands for slant height
Therefore, we can simply plug in all of the given values into the formula to get our answer.
The equation we would solve would be:
SA = 3.14*4*5+3.14*4^2
This gives us 113.04
The answer that is closest to this would be 113
Therefore, the answer is 113
Hope this helped!!C:D
Answers
Answer:
0.111<1.001
1.11 > 1.01
Step-by-step explanation:
To identify the greater number from decimal number.
Rule: First we check number or digits before decimal.
- If digit is greater than number is greater than.
- If digit is smaller then number is smaller
- If digit is same then check digit after decimal.
# 0.111 or 1.001
In 0.111 digit before decimal is 0
In 1.001 digit before decimal is 1
As we know 0<1
So, 0.111<1.001
# 1.11 or 1.01
In 1.11 digit before decimal is 1
In 1.01 digit before decimal is 1
1 = 1 , So test fail. Now check digit after decimal.
In 1.11 digit after decimal is 1
In 1.01 digit after decimal is 0
As we know 1>0
So, 1.11 > 1.01
Infrared
Radio waves
Ultraviolet
Visible light
Answers
Answer:Third option is correct.
Step-by-step explanation:
Certain high-frequency radiations are likely to cause harm to astronauts landing on Mars.
Ultraviolet is the most suitable to study this harmful radiation on Mars.
It has highest frequency than X-rays but shorter than visible rays.
It is harmful is nature as it causes painful sunburns and premature ageing of the skin etc.
Hence, Third option is correct.
Answer:
Given the options: Infrared, Radio waves, Ultraviolet and Visible light, ordering them by frequency (for highest to lowest) we get:
Ultraviolet
Visible light
Infrared
Radio waves
Knowing that high-frequency radiations are likely to cause harm to astronauts landing on Mars, then the detector of Ultraviolet is most suitable
Step-by-step explanation:
Answers
3/4
4/4
5/4
This is the answer I think
Answers
In the given problem, the square root of 1.69 is 1.3.
The square root of a non-negative real number is a value that, when multiplied by itself, results in the original number. In mathematical notation, the square root of the number "x" is represented by the symbol "√x."
The square root is an inverse operation of squaring, which means that if one squares a number and then take its square root, he or she gets back to the original value. The concept of the square root is nearly related to obtaining the side length of a square with a given area or obtaining the magnitude of a vector in mathematics.
1.69 also can be written as in fraction form.
Thus, 1.3 is the square root of 1.69.
Learn more about square roots here:
#SPJ6
48 25 39 64 70 65 52 43 21 22
46 28 39 76 63 39 42 55 29 30
A.
The frequency table should not have been set up in intervals.
B.
The recorded frequency for the interval 40 - 49 is incorrect.
C.
The recorded frequency for the interval 70 - 79 is incorrect.
D.
The frequency table is correct.
Answers
The recorded frequency for the interval 70 - 79 is incorrect, option C is correct.
What is Statistics?
Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We can find the frequency for each interval by counting the number of data points that fall within each range.
There are no values between 10 and 19, so the frequency of 1 for the interval 10-19 is correct.
Similarly, there are no values between 50 and 59 or between 60 and 69, so the frequencies of 4 for the intervals 50-59 and 60-69 are correct.
when we count the values between 40 and 49 the range is 5 which is correct.
when we count the values between 70 and 79, we see that there are 3 value in this range, not 2 as listed in the frequency table.
Hence, the recorded frequency for the interval 70 - 79 is incorrect.
To learn more on Statistics click:
#SPJ2
It's C I took the quiz