Garden one has 9 more bushes of red currant than garden two. If 3 bushes were transplanted from garden two to garden one, then g

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Garden one has 9 more bushes of red currant than garden two. If 3 bushes were transplanted from garden two to garden one, then g

arden one would have 1.5 times more bushes than garden two. How many currant bushes are there in garden one?

Mathematics

2 answers:

Vesnalui [34] · Answer 1 · 2022-06-05T13:06:56+03:00

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

Fynjy0 [20] · Answer 2 · 2022-06-05T14:31:18+03:00

Garden one has $\boxed{42}$ currant bushes.

Further Explanation:

Consider $y$ be the number of currants in garden one.

Consider $x$ be the number of currants in garden two.

According to the question garden one has $9$ more currants than garden two.

Therefore, the number of currants in garden one is $x+9$ and the number of currants in garden $2$ is $x$ .

If $3$ bushes were transplanted from garden two to garden one

Then, garden two has $x-3$ currants and garden one has $x+12$ .

Garden one would have $1.5$ times more bushes than garden two.

The expression of the above statement can be expressed as,

$\begin{aligned}1.5\left( {x - 3} \right)&= x + 12 \\1.5x - 4.5&= x + 12 \\1.5x - x&= 12 + 4.5 \\0.5x&= 16.5\\x &= \frac{{16.5}}{{0.5}}\\x &= 33 \\\end{aligned}$