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Annette [7]
3 years ago
9

6 plates and 5 cups cost 32.10 dollars. 7 plates and 6 cups cost 37.70 dollars. Each plate costs the same amount as the other pl

ates, and each cup costs the same amount as the other cups. What is the cost of 1 plate? What is the cost of 1 cup?
Mathematics
2 answers:
slavikrds [6]3 years ago
8 0

Answer:

Plates are 2.80 Dollars and cups are 1.40 dollars

Step-by-step explanation:

Cups = c

Plates = p

6p + 5c = 23.80 ==> multiply by 6 ==> 36p + 30c = 142.80

7p + 6c = 28.00 ==> multiply by 5 ==> 35p + 30c = 140.00

Now use algebra to have the 30c be on one side and the rest on the other:

36p + 30c = 142.80 | -36p

30c = 142.80 - 36p

35p + 30c = 140.00 | -35p

30c = 140.00 - 35p

Now set them equal to each other about the 30c:

142.80 - 36p = 140.00 - 35p

Use algebra to solve for p:

142.80 - 36p = 140.00 - 35p | +36p

142.80 = 140.00 + p | - 140

2.80 = p

Go back to one of the "30c" equations and plug in the value for p:

30c = 140 - 35p

30c = 140 - 35(2.80)

30c = 140 - 98

30c = 42 | /30

c = 42/30

c = 1.4

MrRa [10]3 years ago
3 0

Answer:

the cost of 1 plate  $4.1

the cost of 1 cup $1.5

Step-by-step explanation:

6p + 5c = 32.10

7p + 6c=  37.70

Multiply the first by 6

Multiply the second by -5

and then ADD both

36p +30c = 192.6

-35p-30c =  -188.5   (30c is cancelled)

p = 4.1

4.1(6) +5c = 32.10

24.6 +5c = 32.10

5c = 7.5

c= 1.5

1.5(5) =7.5

24.6 + 7.5 = 32.10

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Answer:

x = approx. 1.24 or -7.24

Step-by-step explanation:

It's hard to factor directly so we should use the quadratic formula or complete the square. I'm going to go with completing the square.

x²+6x-9=0

x²+6x=9

x²+6x is the same as x²+2·3·x, in order to make this into the algebraic identity (A+B)²=A²+2AB+B², we must add B², or in this case 3² to both sides. (A is x, B is 3)

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Write an equation for nth term:

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