Question

A bouquet of 8

Answer 1

A rose costs $2.5 and a carnation costs $3.

Step-by-step explanation:

Let,

Roses = x

Carnations = y

According to given statement;

8x+10y=50  Eqn 1

6x+12y=51    Eqn 2

Multiplying Eqn 1 by 6;

$6(8x+10y=50)\\48x+60y=300\ \ \ Eqn\ 3$

Multiplying Eqn 2 by 8;

$8(6x+12y=51)\\48x+96y=408\ \ \ Eqn 4$

Subtracting Eqn 3 from Eqn 4;

$(48x+96y)-(48x+60y)=408-300\\48x+96y-48x-60y=108\\36y=108$

Dividing both sides by 36;

$\frac{36y}{36}=\frac{108}{36}\\y=3$

Putting y=3 in Eqn 3;

$48x+60(3)=300\\48x+180=300\\48x=300-180\\48x=120$

Dividing both sides by 48;

$\frac{48x}{48}=\frac{120}{48}\\x=2.5$

A rose costs $2.5 and a carnation costs $3.

Keywords: linear equations, subtraction

Learn more about linear equations at:

• brainly.com/question/11007026
• brainly.com/question/11207748

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