Respuesta :
Garden one and two are both unknown, so I am choosing to call garden 2 X and then label garden 1 with comparisons to X.
It is tempting to list:
Garden Two = X
Garden One = X + 9
BUT there is an easier way. We are told that when 3 bushes are taken from garden 2 (x-3) and put in garden 1 (x + 12) then garden one has 1.5 times more than garden two.
Set it up like this:
1.5 ( x - 3) = x + 12 (because 1.5 times garden 2 will give us garden 1)
1.5x - 4.5 = x + 12 (Distribute)
.5x = 16.5 (Use subtraction to move variables to the right and other numb left)
x = 33 for Garden 2
33 + 9 for Garden 1 = 42
Garden one has [tex]\boxed{42}[/tex] currant bushes.
Further Explanation:
Consider [tex]y[/tex] be the number of currants in garden one.
Consider [tex]x[/tex] be the number of currants in garden two.
According to the question garden one has [tex]9[/tex] more currants than garden two.
Therefore, the number of currants in garden one is [tex]x+9[/tex] and the number of currants in garden [tex]2[/tex] is [tex]x[/tex].
If [tex]3[/tex] bushes were transplanted from garden two to garden one
Then, garden two has [tex]x-3[/tex] currants and garden one has [tex]x+12[/tex].
Garden one would have [tex]1.5[/tex] times more bushes than garden two.
The expression of the above statement can be expressed as,
[tex]\begin{aligned}1.5\left( {x - 3} \right)&= x + 12 \\1.5x - 4.5&= x + 12 \\1.5x - x&= 12 + 4.5 \\0.5x&= 16.5\\x &= \frac{{16.5}}{{0.5}}\\x &= 33 \\\end{aligned}[/tex]
Garden two has [tex]\boxed{33}[/tex] currant bushes.
Therefore, garden one has can be calculated as,
[tex]\begin{aligned}x + 9 &= 33 + 8 \\ &= 42\\\end{aligned}[/tex].
Hence, garden one has [tex]\boxed{42}[/tex] currant bushes.
Learn more:
1. Learn more about unit conversion https://brainly.com/question/4837736
2. Learn more about non-collinear https://brainly.com/question/4165000
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: garden, bushes, red currant, garden one, garden two, transplanted, currant, 1.5 times, 9 more bushes of red currant, how many.
