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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)

Respuesta :

rspill6

Answer:

Step-by-step 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.

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