High School

Can someone please complete these two system of equations word problems? Please show your work for both of them.

37. Kim and Shayna each improved their yards by planting hostas and geraniums. They bought their supplies from the same store. Kim spent $135 on 6 hostas and 7 geraniums. Shayna spent $234 on 9 hostas and 14 geraniums. What is the cost of one geranium?

41. Lea and Julio each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same store. Lea spent $74 on 4 rose bushes and 6 geraniums. Julio spent $172 on 11 rose bushes and 12 geraniums. Find the cost of one rose bush and the cost of one geranium.

Answer :

Answer:

The cost of one geranium is $9 and the cost of one rose bush is $8 and the cost of one geranium is $7.

Step-by-step explanation:

37. Let's define the cost of one hosta as x and the cost of one geranium as y.

We can set up two equations based on the information given:

Equation 1: 6x + 7y = 135

Equation 2: 9x + 14y = 234

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 1, solve for x:

6x = 135 - 7y

x = (135 - 7y)/6

Substitute this expression for x into Equation 2:

9((135 - 7y)/6) + 14y = 234

Multiply both sides of the equation by 6 to get rid of the fraction:

9(135 - 7y) + 84y = 1404

1215 - 63y + 84y = 1404

21y = 189

y = 9

Now substitute this value of y back into Equation 1 to solve for x:

6x + 7(9) = 135

6x + 63 = 135

6x = 135 - 63

6x = 72

x = 12

Therefore, the cost of one geranium is $9.

41. Let's define the cost of one rose bush as x and the cost of one geranium as y.

We can set up two equations based on the information given:

Equation 1: 4x + 6y = 74

Equation 2: 11x + 12y = 172

Again, let's use the method of substitution to solve this system of equations.

From Equation 1, solve for x:

4x = 74 - 6y

x = (74 - 6y)/4

Substitute this expression for x into Equation 2:

11((74 - 6y)/4) + 12y = 172

Multiply both sides of the equation by 4 to get rid of the fraction:

11(74 - 6y) + 48y = 688

814 - 66y + 48y = 688

-18y = -126

y = 7

Now substitute this value of y back into Equation 1 to solve for x:

4x + 6(7) = 74

4x + 42 = 74

4x = 74 - 42

4x = 32

x = 8

Therefore, the cost of one rose bush is $8 and the cost of one geranium is $7.

37)

hostas = h
gereniums = g

kim :

6h + 7g = 135

shayna :

9h + 14g = 234

so the equation will be :

6h + 7g = 135 ⇒ (1)
9h + 14g = 234 ⇒ (2)

we will multiply equ(1) by -2
so it will be :

-12h - 14g = -270 ⇒ (1)
9h + 14g = 234 ⇒ (2)

now we will add 1 to 2

-12h + 9h - 14g + 14g = -270 + 234

-3h + 0g = -36

-3h = -36

h = 12

now we will back to the equation (1)
6h + 7g = 135

6(12) + 7g = 135

7g = 135 - 72

7g = 63

g = 63 ÷ 7

g = 9

so the cost of geranium is 9$

the next question will be in the comment


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