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Micaela and Chelsea each improved their yards by planting rose bushes and ivy. They bought their supplies
from the same store. Micaela spent $58 on 5 rose bushes, r, and 3 pots of ivy, i. Chelsea spent $100 on 5
rose bushes and 10 pots of ivy. Write equations to represent the scenario. Then, find the cost of one rose
bush and the cost of one pot of ivy.

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Answer:

Step-by-step explanation:

Let:

i: the cost of one pot of ivy.

r: the cost of one rose bush

[tex]5r+3i=58 ......(1)\\5r+10i=100.......(2)\\\\[/tex]

From eq(1) we can get:

[tex]r=\frac{58-3i}{5} \\[/tex]

Substitute eq(1) in eq(2):

[tex]5(\frac{58-3i}{5})+10i=100\\58-3i+10i=100\\7i=100-58\\i=\frac{42}{7} =6\\[/tex]

[tex]r=\frac{58-3i}{5} \\r=\frac{58-3(6)}{5} \\\\r=8[/tex]

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Answer:  A rose bush, r, cost $8; one pot of ivy, i, cost $6;

Step-by-step explanation:

[tex]\left \{ {{5r + 3i =58} \atop {5r+10i=100}} \right.[/tex]

We combine them by minus, we get:

    5r + 3i = 58

-    5r + 10i = 100

           - 7i = - 42

               i = 6

We plug in i = 6 to the first equation, we get:

     5r + 3(6) = 58

        5r + 18 = 58

                5r = 40

                  r = 8

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