Question

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?

Answer 1

Answer:

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 = $\frac{75}{6}$

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 = $\frac{183}{6}$

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

Answer 2

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.

 $8x+6y=283$ ---------------(1)

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

$10x+12y=491$ ------------------(2)

We need to find the price of a table arrangement.

Solution:

First we solve the equation 1 for x.

 $8x+6y=283$

 $8x=283-6y$

 $x=\frac{283-6y}{8}$

Substitute x value in equation 2.

$10(\frac{283-6y}{8})+10y=491$

Simplify

$\frac{10\times 283}{8}-\frac{10\times 6y}{8} + 12y = 491$

$\frac{2830}{8}-\frac{60y}{8}+12y=491$

Both fraction number divided by 2.

$\frac{1415}{4}-\frac{30y}{2}+12y=491$

$12y-\frac{30y}{4}=491-\frac{1415}{4}$

$\frac{4\times 12y-30y}{4}=\frac{4\times 491-1415}{4}$

$\frac{48y-30y}{4}=\frac{1964-1415}{4}$

Multiply by 4 both side

$4\times\frac{18y}{4}=4\times \frac{549}{4}$

$y=\frac{549}{18}$

Both numerator and denominator divided by 9.

$y=\frac{61}{2}$

$y=30.5$

Therefore, the price of a table arrangement is $30.5