Last weekend, she collected $283 from selling 8 bouquets and 6 table arrangements. the week before, she collected $491 from selling 10 bouquets and 12 table arrangements. what is the price of a table arrangement?

The price of each table arrangement is $30.5

Step-by-step explanation:

Given as :

The Amount collected from selling 8 bouquets and 6 table arrangement = $283

The Amount collected from selling 10 bouquets and 12 table arrangement = $491

Let The price of each bouquets = $b

Let The price of each table arrangement = $a

According the question

Number of bouquets sold × price of each bouquets + number of table arrangement sold × price of each table arrangement = Total amount collected

i.e 8 b + 6 a = $283              .......A

And

10 b + 12 a = $491                  ............B

Now, Solving equation a and B

2 × (8 b + 6 a) - (10 b + 12 a) = 2 × 283 - 491

Or, 16 b + 12 a - 10 b - 12 a = 566 - 491

Or, (16 b - 10 b) + (12 a - 12 a) = 75

Or, 6 b + 0 = 75

∴  b =

i.e b = $12.5

So, The  price of each bouquets = b = $12.5

Put the value of b in eq A

∵ 8 b + 6 a = $283  

i.e 8 × 12.5 + 6 a = $283

Or, $100 + 6 a = $283

Or, 6 a = $283 - $100

Or, 6 a = $183

∴ a =

i.e a = $30.5

So, The price of each table arrangement  = $30.5

Hence, The price of each table arrangement is $30.5  Answer

Price of a table arrangement = $30.5

Step-by-step explanation:

Let x be the bouquets and y be the table

Given:

she collected $283 from selling 8 bouquets and 6 table arrangements, so the equation is.

 ---------------(1)

The week before, she collected $491 from selling 10 bouquets and 12 table arrangements, so the second equation is written as.

------------------(2)

We need to find the price of a table arrangement.

Solution:

First we solve the equation 1 for x.

Substitute x value in equation 2.

Simplify

Both fraction number divided by 2.

Multiply by 4 both side

Both numerator and denominator divided by 9.

Therefore, the price of a table arrangement is $30.5

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