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BabaBlast [244]
3 years ago
8

Margaret and Kevin each improved their yards by planting rose bushes and daylilies. They bought their supplies from the same sto

re. Margaret spent $74 on 7 rose bushes and 6 daylilies. Kevin spent $24 on 7 rose bushes and 1 daylily. Find the cost of one rose bush and one daylily
Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
5 0

The cost of one rose bush is $2 and one day lily is $10.

Step-by-step explanation:

Let,

Cost of one rose bush = x

Cost of one day lily = y

According to given statement;

7x+6y=74       Eqn 1

7x+y=24         Eqn 2

Subtracting Eqn 2 from Eqn 1

(7x+6y)-(7x+y)=74-24\\7x+6y-7x-y=50\\5y=50

Dividing both sides by 5

\frac{5y}{5}=\frac{50}{5}\\y=10

Putting y=10 in Eqn 1

7x+6(10)=74\\7x+60=74\\7x=74-60\\7x=14

Dividing both sides by 7

\frac{7x}{7}=\frac{14}{7}\\x=2

The cost of one rose bush is $2 and one day lily is $10.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/8955867
  • brainly.com/question/9045597

#LearnwithBrainly

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How to solve your problem

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Simplify

1

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3 years ago
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You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar
Verizon [17]

Answer:

Length=10.5\ ft

Width=10.5\ ft

Area=110.25\ ft^{2}

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

P=2(x+y)

we have

P=42\ ft

so

42=2(x+y)

simplify

21=(x+y)

y=21-x------> equation A

Remember that the area of rectangle is equal to

A=xy ----> equation B

substitute equation A in equation B

A=x(21-x)

A=21x-x^{2}----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

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using a graphing tool

The vertex is the point (10.5,110.25)

see the attached figure

so

x=10.5\ ft

Find the value of y

y=21-10.5=10.5\ ft

The garden is a square

the area is equal to

A=(10.5)(10.5)=110.25\ ft^{2} ----> is equal to the y-coordinate of the vertex is correct

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Answer:

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