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harina [27]
2 years ago
13

Angi has 32 nickels and dimes. Their total value is $1.90. How many of each coin does she have?

Mathematics
1 answer:
Radda [10]2 years ago
5 0

Answer:

6 dimes, 26 nickels

Step-by-step explanation:

The number of nickels is N, and the number of dimes is D.

N + D = 32

5N + 10D = 190

--

N + 2D = 38

D = 6

N = 26

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The sum of the first three terms in a GP is 38.Their product is 1728.Find the values of the three terms.
dusya [7]

Answer:

The value of the three terms is 8 and 18

Step-by-step explanation:

Let "a" be the first term and "r" be the common ratio.

Then from the condition, we have these two equations

   a + ar + ar^2  =   38,      (1)

   a*(ar*)*(ar^2) = 1728.      (2)

From equation (2),  a^3*r^3 = 1728,  or  (ar)^3 = 1728,   which implies

   ar = root%283%2C1728%29 = 12;          (3)    

hence,  

   r  = 12%2Fa.                   (4)

Now, in equation (1) replace the term  ar  by 12, based on (3).  You will get

   a + 12 + ar^2 =  38,   which implies

   a + ar^2 = 26.              (5)

Next, substitute  r = 12%2Fa  into equation (5), replacing "r" there.  You will get

   a + a%2A%28144%2Fa%5E2%29 = 26,   or

   a + 144%2Fa = 26.

Multiply by "a" both sides and simplify

   a^2 - 26a + 144 = 0,

   %28a-13%29%5E2 - 169 + 144 = 0

   %28a-13%29%5E2 = 25

   a - 13 = +/- sqrt%2825%29 = +/- 5.

Thus two solutions for "a" are  a = 13 + 5 = 18  or  a = 13 - 5 = 8.

If  a =  8, then from (4)  r = 12%2F8 = 3%2F2.

If  a = 18, then from (4)  r = 12%2F18 = 2%2F3.

   

In the first case, if a = 8,  then the three terms are  8, 8%2A%283%2F2%29 = 12  and  8%2A%283%2F2%29%5E2 = 18.

   In this case, the sum of terms is  8 + 12 + 18 = 38, so this solution does work.

In the second case, if a = 18,  then the three terms are  18, 18%2A%282%2F3%29 = 12  and  18%2A%282%2F3%29%5E2 = 8.

   In this case, the sum of terms is  18 + 12 + 8 = 38, so this solution does work, too.

ANSWER.  The problem has two solution:  

        a)  first term is 18;  the common difference is 2%2F3  and the progression is  18, 12, 8.

        b)  first term is  8;  the common difference is 3%2F2  and the progression is   8, 12, 18.

4 0
2 years ago
Which of the following expressions represents "no more than 5"? x < 5 x ≤ 5 x > 5 x ≥ 5
diamong [38]
No more then 5..
x < = 5 (thats less then or equal to)
3 0
3 years ago
Read 2 more answers
What is the probability of meeting someone born in January or December (Assume there are 365days in a year)
Karolina [17]
The answer is 62/365 i got
3 0
3 years ago
Justin wants to fence in his yard for his dog. He lives on a rectangular lot 48 feet long and 62 feet wide. How much fencing doe
Alenkasestr [34]
48 X  2 = 96
62 X 2 = 124
124+96 = 220
You could also do it this way:
P = 2(W + L) 
<span>P = 2(48 + 62) </span>
<span>P = 2(110) </span>
<span>P = 220 feet </span>
7 0
3 years ago
Help Plis.........................
strojnjashka [21]

Answer: Herba has a greater balance and Nour has more debt.

Step-by-step explanation: Herba's account balance is a positive number and is clearly greater than Nour's account balance; therefore, Herba has a much greater balance. On the other hand, Nour's account balance is a negative number and is clearly less than Herba's; therefore, Hour is in more debt since he has to pay back the money that he borrowed.

4 0
2 years ago
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