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
sleet_krkn [62]
3 years ago
15

Please explain the process!

Mathematics
1 answer:
galben [10]3 years ago
5 0

Answer:

He correctly determines that she has <u>300</u> nickels and <u>330</u> dimes.

Step-by-step explanation:

I'll first explain how Mark got that system of equations. Then I'll solve the system of equations to find the numbers of coins.

Moira has a collection of nickels and dimes. We don't know the number of nickels and the number of dimes she has.

First, we define two variables to represent the unknowns in this problems, the numbers of coins.

Let n = number of nickels.

Let d = number of dimes.

The sum of the numbers of coins is n + d. We are told she has 630 coins, so the first equation is

n + d = 630

Since we have two unknowns, we need two equations. Now we write an equation based on the values of the coins. A nickel is worth $0.05. A dime is worth $0.1. n nickels are worth 0.05n, and d dimes are worth 0.1d. The total value of the coins is 0.05n + 0.1d. We are told the value of the coins is $48. Now we can write the second equation.

0.05n + 0.1d = 48

Our system of equations is:

n + d = 630

0.05n + 0.1d = 48

These are the same equations Mark got.

Now we solve the system of equations. We will use the substitution method. First, we solve one equation for one variable. Then we substitute that into the other equation.

Let's solve the first equation for n:

n + d = 630

Subtract d from both sides:

n = 630 - d

Now that we know that n is the same as 630 - d, we replace n of the second equation with 630 - d.

0.05n + 0.1d = 48

0.05(630 - d) + 0.1d = 48

Distribute the 0.05:

31.5 - 0.05d + 0.1d = 48

Combine the terms in d:

0.05d + 31.5 = 48

Subtract 31.5 from both sides.

0.05d = 16.5

Divide both sides by 0.05.

d = 330

Now that we know d is 330, we substitute d with 330 in the first original equation and solve for n.

n + d = 630

n + 330 = 630

Subtract 330 from both sides.

n = 300

Since we let n = the number of nickels, and d = the number of dimes, now we can fill in the blanks.

n = number of nickels = 300

d = number of dimes = 330

Answer: He correctly determines that she has <u>300</u> nickels and <u>330</u> dimes.

*******************************************************************

The question is already answered, but we can check with the given information to confirm that our answer is correct.

We check the number of coins:

300 nickels + 330 dimes = 630 coins (the number of coins checks out.)

Now, we check the value of the coins:

300 * $0.05 + 330 * $0.1 = $15 + $33 = $48 (the value of the coins checks out.)

Since both the number of coins and the value of coins check correctly, our answer, 300 nickels and 330 dimes, is correct.

You might be interested in
Susan received $27 for 6 hours of work. Ricky received $14.25 for 3 hours of work. Which statement is true about there hourly ra
8090 [49]

Answer: C. Rickys rate was 0.25 more per hour" .

Step-by-step explanation:

Susan received $27 for 6 hours of work. Susan's rate we hour will be:

= $27/6

= $4.5

Ricky received $14.25 for 3 hours of work. Ricky's rate will be:

= $14.25/3

= $4.75

From the option given, the correct option is C "Rickys rate was 0.25 more per hour" .

This is because $4.75 - $4.5 = $0.25

3 0
2 years ago
A store is instructed by corporate headquarters to put a markup of 25​% on all items. An item costing ​$24 is displayed by the s
larisa [96]

Answer: The correct selling price is $29.97.

Step-by-step explanation:

Since we have given that

Cost price of an item = $27

Mark up rate = 11%

So, Amount of mark up would be

So, Amount after mark up would be

Hence, the correct selling price is $29.97.

The manager's likely error is that he has put the selling price the mark up amount only i.e $2.9≈$3 instead of adding the mark up amount to the cost price.

5 0
3 years ago
Read 2 more answers
Patrick’s luck had changed over night – but not his skill at mathematical reasoning. The day after graduating from college he us
Verdich [7]

Answer:

I assume Josh and Peyton are his friends and both gave him advice on what to do with half of the money from the big lottery win.

Let's say Josh said "save it or invest it for your retirement" and Peyton said "use it to keep playing the lottery.

We will now look at the sense in each piece of advice!

Step-by-step explanation:

JOSH

By investing the $250,000 (half of the money won), Patrick will be sure that the money is available for him anytime and would even have gotten interest, by the time he's ready to use it.

PEYTON

By playing the lottery continuously, Patrick could get lucky once in a while and win big again. How big though?

Analyzing with the figures given,

$20 gets Patrick a lottery ticket.

$250,000 will get him 12,500 lottery tickets!

Whether he's buying the tickets at once or he'll play the lottery once in a while, I'll say he has good chances of winning big again.

So if the probability of winning big after purchasing up to 12,500 tickets is close to 1, Patrick should play the lottery with the $250,000

If the probability of winning big after purchasing 12,500 lottery tickets is close to 0 (closer to 0 than it is to 1) then Patrick should invest the $250,000 in retirement.

5 0
3 years ago
Find the zeros of f(x) = x^2+5x-6.<br> A. {-2,3}<br> B. {-6,1}<br> c. {-2,-3}<br> D. {-6,-1}
Arisa [49]

Answer:

x^2+5x-6

a = 1  b = 5 and c = -6

Using the quadratic formula:

x = [-5 +- sq root (25 -4 * 1 *-6) ] / 2 * 1

x = [-5 +- sq root (49)] / 2

x = [-5 +- 7] / 2

x1 = 1

x2 = -6

Step-by-step explanation:

7 0
3 years ago
What is 2/9s of 630
maria [59]

Answer: its 18.27  

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Other questions:
  • given the equation -4 square root of x-3=12, solve for x and identify if it is an extraneous solution
    7·1 answer
  • William Gay for football cards to each of his friends suppose he had 454 cars left write and solve an equation to determine how
    14·1 answer
  • I Really Need Help With This Problem, Please
    10·2 answers
  • Which ratio is greater than 5/8 , A. 12/24 B. 3/4 C. 15/24 D.4/12
    7·2 answers
  • How many more players are 49 1/2 inches than 46 1/2 inches tall?
    6·1 answer
  • PLEASE HELP ITS ATEST I BEG U. NEED HELP
    13·2 answers
  • If the probability that it will rain tomorrow is , what is the probability that it will not rain tomorrow? ASAP
    7·2 answers
  • A square of 81cm² is cut to make two rectangles, A and B
    15·2 answers
  • I’m gonna be asking a lot of these so if your good at these then watch out for more! :)
    10·2 answers
  • Look at the picture below thank you
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!