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Luda [366]
3 years ago
15

A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 8 tables is $58. The total cost to re

nt 5 chairs and 2 tables is $23. What is the cost to rent each chair and each table?
Mathematics
1 answer:
schepotkina [342]3 years ago
7 0

Answer:

Equations::

4c + 8t = 58

2c + 3t = 23

----------------

Modify for elimination:

4c (4c*1) + 8t (8t*1)= 58

4c (2c*2) + 6t (3t*2)= 46

---------------------

Subtract and solve for "t":

2t (8t-6t) = 12

t = $6 (cost of one table)

-----

Solve for "c":

2c + 3t = 23

2c + 18 = 23

2c = 5

c = $2.50 (cost of one chair)

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Answer:

a = -2

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Step-by-step explanation:

5a+3b=11

-2a+3=b

substitute for b:

5a + 3(-2a + 3) = 11

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Show work and explain with formulas:
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17 Answer:  205

<u>Step-by-step explanation:</u>

\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n

\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}

18 Answer:  1968

<u>Step-by-step explanation:</u>

a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88

\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}

19 Answer:  -116

<u>Step-by-step explanation:</u>

\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}

6 0
3 years ago
I need help on .5 and .6
Dovator [93]
5. 44 (forty four)
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8 0
3 years ago
Plz help with math u will get Brainliest
emmasim [6.3K]

Answer:

Volume = 315 cm³

Step-by-step explanation:

Volume = Length × Width × Height

→ Substitute in the values

Volume = 6 cm × 3.5 cm × 15 cm

→ Simplify

Volume = 315 cm³

4 0
3 years ago
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