Jaidee and Willie each improves their yards by planting rose bushes and geraniums. They bought their supplies from the same stor

Question

4 years ago

7

Jaidee and Willie each improves their yards by planting rose bushes and geraniums. They bought their supplies from the same stor

e. Jaidee spent $84 on 3 rose bushes and 12 geraniums. Willie spent $120 on 8 rose bushes and 6 geraniums. Find the cost of one rose and the cost of one geranium

Mathematics

1 answer:

stiks02 [169] · Answer 1 · 2022-01-14T06:35:40+03:00

The cost of one rose bush is $12 and cost of one geranium is $4.

Step-by-step explanation:

Let,

Cost of one rose = x

Cost of one geranium = y

According to given statement;

3x+12y=84 Eqn 1

8x+6y=120 Eqn 2

Multiplying Eqn 2 by 2

$2(8x+6y=120)\\16x+12y=240\ \ \ \ Eqn\ 3$

Subtracting Eqn 1 from Eqn 3

$(16x+12y)-(3x+12y)=240-84\\16x+12y-3x-12y=156\\13x=156\\$

Dividing both sides by 13

$\frac{13x}{13}=\frac{156}{13}\\x=12$

Putting x=12 in Eqn 1

$3(12)+12y=84\\36+12y=84\\12y=84-36\\12y=48$

Dividing both sides by 12

$\frac{12y}{12}=\frac{48}{12}\\y=4$

The cost of one rose bush is $12 and cost of one geranium is $4.

Keywords: linear equation, subtraction

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