Both sunflowers will have same height after 8 weeks
Step-by-step explanation:
Let w be the number of weeks
Then
a sunflower with a height of 8 cm that grows at a rate of 3 1/2 cm per week
[tex]8+3\frac{1}{2}w\\=8+\frac{7}{2}w[/tex]
And
a sunflower with a height of 10 cm that grows at a rate of 3 1/4 cm per week.
[tex]10+3\frac{1}{4}\\=10+\frac{13}{4}w[/tex]
In order to find the number of weeks when both plants will have same height we will put the expressions for both equal
So,
[tex]8+\frac{7}{2}w = 10+\frac{13}{4}w[/tex]
Subtracting 8 from both sides
[tex]8-8+\frac{7}{2}w = 10-8+\frac{13}{4}w\\\frac{7}{2}w = 2+\frac{13}{4}w[/tex]
Subtracting 13/4 from both sides
[tex]\frac{7}{2}w-\frac{13}{4}w = 2+\frac{13}{4}w-\frac{13}{4}w\\\frac{14-13}{4}w = 2\\\frac{1}{4}w = 2[/tex]
Multiplying both sides by 4
[tex]w = 8[/tex]
So,
Both sunflowers will have same height after 8 weeks
Keywords: Linear equations, variables
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