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docker41 [41]
3 years ago
9

A collection of quarters and nickels is worth ​$3.75. There are 27 coins in all. Find how many of each there are.

Mathematics
1 answer:
inysia [295]3 years ago
6 0

Q +N =27

Q=27-N

0.25Q + 0.05N =3.75

0.25(27-N) + 0.05 =3.75

6.75-0.25N+0.05N=3.75

6.75-0.2N=3.75

-0.2N=-3

N=-3/-0.2 = 15

15 nickels

27-15 = 12

12 quarters

15x0.05 = 0.75

12 x 0.25 = 3.00

3.00 + 0.75 = 3.75


 12 quarters & 15 nickels

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The total number of people at a football game was 5600. Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.
rewona [7]

Answer:

1100 field-side tickets and 4500 end-zone tickets.

Step-by-step explanation:

Let x represent number of field side tickets and y represent number of end-zone tickets.

We have been given that the total number of people at a football game was 5600. We can represent this information in an equation as:

x+y=5600...(1)

y=5600-x...(1)    

We are also told that Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.

Cost of x field side tickets would be 40x and cost of y end-zone tickets would be 20y.

The total amount of money received for the tickets was $134000. We can represent this information in an equation as:

40x+20y=134000...(2)

Upon substituting equation (1) in equation (2), we will get:

40x+20(5600-x)=134000

40x+112000-20x=134000

20x+112000=134000

20x+112000-112000=134000-112000

20x=22000

\frac{20x}{20}=\frac{22000}{20}

x=1100

Therefore, 1100 field side tickets were sold.

Upon substituting x=1100 in equation (1), we will get:

y=5600-1100

y=4500

Therefore, 4500 end-zone tickets were sold.

3 0
3 years ago
Solve this system of linear equations. Separate
alex41 [277]

Answer:

y = 7 and x =3

Step-by-step explanation:

use elimination method

so we gonna eliminate y first

9x = 1 - 4y

-7x = -7 + 4y

7| 9x = 1 - 4y

9| -7x = -7 + 4y

63x = 7 - 28y

-63x = -63 + 36y

add eqtn 1 to eqtn2

you will get

0 = -56 + 8y

56 = -56 + 56 + 8y

56 = 8y

56÷8 = 8y÷ 8

7 = y

also eliminate x as we have done wth y

4| 9x = 1 - 4y

4| -7x = -7 + 4y

36x = 4 - 16y

-28x = -28 + 16y

add the two equations

u will get

8x = -24 + 0

8x = -24

8x÷8 = 24÷ 8

x = 3

5 0
3 years ago
WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST AND CORRECT PLEASE EXPLAIN WHY YOU ARE CORRECT
Sholpan [36]

Answer:

In a typical kite as shown in picture, it is symmetric around PQ and PQ is perpendicular with RN.

=> Two right triangles PNT and PRT are congruent.

=> angle PRT = angle PNT = 34 deg

=> angle RPT = 90 - angle PRT = 90 - 34 = 56 deg

=> Option A is correct.

Hope this helps!

:)

4 0
3 years ago
Read 2 more answers
Determine which of these sequences is an arithmetic sequence. Then determine the explicit formula that would be used to define t
vagabundo [1.1K]

6)

34, 43, 52, 61, ...

43-34 = 9; 52-43 = 9; 61-52 = 9

The difference between one term and the next is a constant so it is arithmetic sequence

first term:  a = 34

difference:  d = 9

so the formula:

                         a_n=a+d(n-1)\\\\a_n=34+9(n-1)\\\\a_n = 34+9n-9\\\\\underline{a_n=9n+25}

7)

10, 6, 2, -2, ...

6-10 = -4; 2-6 = -4; -2-2 = -4

The difference between one term and the next is a constant so it is arithmetic sequence

first term:  a = 10

difference:  d = -4

so the formula:

                         a_n=a+d(n-1)\\\\a_n=10+(-4)(n-1)\\\\a_n = 10-4n+4\\\\\underline{a_n=-4n+14}

8)

-3, -10, -17, -24, ...

-10-(-3) = -7; -17-(-10) = -7; -24-(-17) = -7

The difference between one term and the next is a constant so it is arithmetic sequence

first term:  a = -3

difference:  d = -7

so the formula:

                         a_n=a+d(n-1)\\\\a_n=-3+(-7)(n-1)\\\\a_n =-3-4n+7\\\\\underline{a_n=-7n+4}

9)

7, 8.5, 10, 11.5, ...

8.5-7 = 1.5; 10-8.5 = 1.5; 11.5-10 = 1.5

The difference between one term and the next is a constant so it is arithmetic sequence

first term:  a = 7

difference:  d = 1.5

so the formula:

                         a_n=a+d(n-1)\\\\a_n=7+1.5(n-1)\\\\a_n =7+1.5n-1.5\\\\\underline{a_n=1.5n+5.5}

10)

30, 22¹/₂, 15, 7¹/₂, ...

22¹/₂-30 = -7¹/₂;   15-22¹/₂ = -7¹/₂;   7¹/₂-15 = -7¹/₂

The difference between one term and the next is a constant so it is arithmetic sequence

first term:  a = 30

difference:  d = -7¹/₂

so the formula:

                         a_n=a+d(n-1)\\\\a_n=30+(-7\frac12)(n-1)\\\\a_n =30-7\frac12n+7\frac12\\\\ \underline{a_n=-7\frac12n+37\frac12}

6 0
3 years ago
Helen had $12 but spent $3 of it. What per cent did she spend?
Bezzdna [24]

Answer:

25%

Step-by-step explanation:

Its basic division really. The easiest way to think of it is how many times can 3 fit into 12 three fits into 12 four times in fraction that's 1/4 or 1 over 4. Just like the quarter (United States quarter) each one is 25 cents and you need 4 of then to make 1 US dollar or 100% so each group of three is 25 percent. This under standing could work with a variety of numbers 5 is what percent of 20 or 7 is what percent of 28 if it comes in 4s each is 25%. Hope this helps.

4 0
3 years ago
Read 2 more answers
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