Question

Micaela and Elisa each improved their yards by planting rose

bushes and geraniums. They bought their supplies from the
same store.
Micaela spent $122 on 14 rose bushes and 8 geraniums.
Elisa spent $120 on 12 rose bushes and 12 geraniums.
What is the cost of one geranium?

• $1
• $7
• $3
• $5

Answer 1

Let x be the cost of roses and y be the cost of geraniums
122 = 14x + 8y
120 = 12x + 12y
1) solve for a variable
We can use second equation to find x and plug it in in terms of y
10 = x + y
X = 10 - y
2) plus it into first equation
122= 14(10 - y) + 8y
122 = 140 - 14y + 8y
6y = 18
Y = 3

Answer 2

One geranium is $3

Explanation:

Let r = roses and g = geraniums

14r + 8g = 122

12r + 12g = 120

Multiply first equation by -3 and the second by 2 (we are trying to get terms that cancel when we add the two equations)

-42r - 24g = -366

+24r + 24g = 240

Add

18r = 126

r = 7, so one rose is $7

Put this into either of the original equations

14(7) + 8g = 122

98 +8g = 122

8g = 24

g = 3, so one geranium is $3