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TiliK225 [7]
3 years ago
13

Janet has three times as many dimes as nickels and twice as many quarters as nickels. If she has $5.10 in all, how many nickels,

dimes, and quarters does she have? If n represents the number of nickels Janet has, which of the following equations could be used to solve the problem?
a). 5n + 10n + 25n = 510
b). n + 3n + 2n = 510
c). 5n + 30n + 50n = 510
Mathematics
1 answer:
Mama L [17]3 years ago
6 0
If number of nickel = n
number of dimes = 3n
number of quarters = 2n

Amount of nickel = 5n
Amount of dimes = 30n
Amount of quaters = 50n

Total Amount = <span>5n + 30n + 50n = 510

In short, Your Answer would be Option C

Hope this helps!</span>
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A linear equation in two variables has infinitely many solution the set of all solutions to a linear equation in two variables f
Greeley [361]
<span>1, During a 1-hr television program, there were 22 commercials, Some commercials were 15 sec and some were 30 sec long. Find the number of 15- sec commercials and the number of 30 sec commercial if the total playing time for commercial was 9.5 minutes.

</span>a) <span>show how to formulate your system of equations for your problem,

Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language

b) state the two equations:

- translate the word statement into algebraic equations:

</span><span>* there were 22 commercials => x + y = 22
* the total playing time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>

Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y =  570

c) state which method you will use to solve either addition or substitution

Answer:
adition: multiply the first equation times - 15 and add the two equations.

d) solve your system showing and explaining each step of the process

Answer:
- muliply eq (1) times - 15

-15x - 15y = - 330

- add that to the eq (2):

-15x + 15x - 15y + 30y = -330 + 570

- add like terms: 15y = 240

- divide both members by 15: 15y/15 = 240 / 15 => y = 16

- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6

Solution: x = 6, y = 16

e) Be sure to check your solution!

x + y = 22
6 + 16 = 22
22 = 22 --> check

15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check

f) Once a solution is found explain what this solution means in the context of the problem, write the answer to the word problem in words</span><span>

The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.

2, How many quarts of water should be mixed with a 30% vinegar solution to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>

a) variables:

- state the variables
x: number of quarters of water
y: number of quarters of vinegar

- translate the words into mathematical language

12 qt 25% vinegar solution

=> total number of quarts = 12 = x + y

balance in vinegar:

vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution

0 + 0.3y = 0.25 (x + y)

c) Equations

Eq (1) x + y = 12

Eq (2): 0.3y = 0.25x + 0.25y

=> 0.25x - 0.05y = 0

d) solve

- multiply eq (1) times 0.05 and add to eq (2)

0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6

x = 0.6 / 0.3 = 2

x + y = 12 => y = 12 - y = 12 - 2 = 10

Solution: x = 2, y = 10

e) check:

x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check

vinegar:

10*0.3 = 12*0.25
3 = 3 -> check

f) Explanation of the solution

The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.

5 0
3 years ago
Whats the answer giving brainliest&gt;&gt;&gt;&gt;
Elza [17]

Answer:

the answer is b

Step-by-step explanation:

brainliest pls

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3 years ago
an employee adds 160 fluid ounces of chemical to a feature that holds 120,000 gallons of water. did the employee add yhe correct
Hitman42 [59]
We are given a volume of 160 fluid ounces of chemical which is added to a container that holds 120,000 gallons of water. Assuming that the chemical has the same density as water, we just need to convert 120,000 gallons to ounces.

A conversion factor is taken from literature, 1 gallon is equivalent to 128 fluid ounces. So 160 fluid ounces is only 1.25 gallons, thus occupying minimal space in the container. The employee could add more of the chemical in the container. He can actually add 15360000 fluid ounces in total. 
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3 years ago
A plant 3 in. tall grows an average of 0.5 in. each month. Which equation models the flowers height h after x months?
Luden [163]

Answer:the answer is b

Step-by-step explanation:

i cant really explain how i know its kind of second natural to me now

7 0
3 years ago
Identify the solution(s) of the system of equations, if any.<br> -6x - 4y = 12<br> 12y = -18x - 36
UkoKoshka [18]
-6x - 4y = 12|\div 2\\&#10;12y = -18x - 36|\div 6\\\\&#10;-3x-2y=6\\&#10;2y=-3x-6\\\\&#10;-3x-2y=6\\&#10;-3x-2y=6

Both equations are equivalent, so there are infinitely many solutions.
5 0
3 years ago
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