Question

3) Abhasra and Lisa each improved their yards by planting rose bushes and geraniums. They

bought their supplies from the same store. Abhasra spent $219 on 30 rose bushes and 11
geraniums. Lisa spent $420 on 6 rose bushes and 44 geraniums. Find the cost of one rose bush
and the cost of one geranium.

(EXPLAIN HOW DONE)

Answer 1

Explanation:

Let R and G stand for the prices of rose bushes and geraniums, respectively.

We are told that:

Abhasra: 30R + 11G = $219

Lisa: 6R + 44G = $420

Two equations and two unknowns. Eliminate one of the variables by substitution:

Let's start with

6R + 44G = $420

and try to eliminate the G. We note that the first equation, 30R + 11G = $219, can be multiplied by 4 to bring the geraniums up to the same as in the second equation:

6R + 44G = $420

4*(30R + 11G = $219) = 120R + 44G = 876

Now subtract this equation from the first:

6R + 44G = $420

-120R - 44G = -$876

-114R = -456

R = 4: Rose bushes are $4 each.

Now use R= $4 in either equation to find G:

6R + 44G = $420

6($4) + 44G = $420

$24 + 44G = $420

44G = $396

G = : Geraniums are $9.00 each.