A bouquet of 8
roses and 10 carnations costs $50. A bouquet of 6 roses and 12 carnations costs $51. How much do one rose and one carnation cost?

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absor201 absor201 · Answer 1 · 2019-12-01T09:46:10+01:00

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;

[tex]6(8x+10y=50)\\48x+60y=300\ \ \ Eqn\ 3\\[/tex]

Multiplying Eqn 2 by 8;

[tex]8(6x+12y=51)\\48x+96y=408\ \ \ Eqn 4[/tex]

Subtracting Eqn 3 from Eqn 4;

[tex](48x+96y)-(48x+60y)=408-300\\48x+96y-48x-60y=108\\36y=108[/tex]

Dividing both sides by 36;

[tex]\frac{36y}{36}=\frac{108}{36}\\y=3[/tex]

Putting y=3 in Eqn 3;

[tex]48x+60(3)=300\\48x+180=300\\48x=300-180\\48x=120[/tex]

Dividing both sides by 48;

[tex]\frac{48x}{48}=\frac{120}{48}\\x=2.5[/tex]

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

Keywords: linear equations, subtraction

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