Kim and Kristin each improved their yards by planting hostas and geraniums. They bought their supplies from the same store. Kim spent $92 on 13 hostas and 3 geraniums. Kristin spent $156 on 6 hostas and 14 geranium. Find the cost of one hostas and the cost of one geranuim.

Question

contestada

Respuesta :

absor201 absor201 · Answer 1 · 2019-12-21T10:08:05+01:00

Cost of one hosta is $5 and cost of one geranium is $9.

Step-by-step explanation:

Let,

Cost of one hosta = x

Cost of one geranium = y

According to given statement;

13x+3y=92 Eqn 1

6x+14y=156 Eqn 2

Multiplying Eqn 1 by 6

[tex]6(13x+3y=92)\\78x+18y=552\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 13

[tex]13(6x+14y=156)\\78x+182y=2028\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 3 from Eqn 4

[tex](78x+182y)-(78x+18y)=2028-552\\78x+182y-78x-18y=1476\\164y=1476[/tex]

Dividing both sides by 164

[tex]\frac{164y}{164}=\frac{1476}{164}\\y=9[/tex]

Putting y=9 in Eqn 2

[tex]6x+14(9)=156\\6x+126=156\\6x=156-126\\6x=30[/tex]

Dividing both sides by 6

[tex]\frac{6x}{6}=\frac{30}{6}\\x=5[/tex]

Cost of one hosta is $5 and cost of one geranium is $9.

Keywords: linear equation, subtraction

Learn more about linear equations at:

#LearnwithBrainly