Question

The ratio of the number of tomato plants in Inessa’s garden to the number of tomato plants in Ralph’s garden was 5:6. After 1/2 the tomato plants from Inessa’s garden were replanted in Ralph’s garden, Ralph’s garden had 850 tomato plants. How many tomato plants did Ralph’s garden have in the first place?

Answer 1

let "x" represent the number of units
5x = the number of tomato plants in Inessa's garden
6x = the number of tomato plants in Ralph's garden

the question says that half (1/2 x (5x)) of Inessa's tomato plants are taken from her garden and put into Ralph's garden 
this means that Ralph has a total of 850 tomato plants in his garden

using all of this information, we get the following (which we have to solve):
(1/2)(5x) + 6x = 850

when we solve for "x", we find that:
"x" = 100

so, going back to the original statement, if Ralph started out with (6x) tomato plants, and "x" = 100, we have to multiply 6 by 100

doing so gives us our final answer:
Ralph had 600 tomato plants in the beginning

I hope this helps! :D

Answer 2

Ratio can be said as a comparison of two numbers which can be expressed by using ":" sign between two or more numbers or data. The relative sizes of two or more values is represented by ratios.

In the given question the ratio of plants in Inessa's garden to the ratio of plants in Ralph's garden is given and we have to determine the number of plants of Ralph's garden.

Given

Ratio of plants in gardens of Ralph and Inessa is 5:6

Half of Inessa's plants were replanted in Ralph's garden.

Ralph's garden now have 850 plants.

Calculation

Let the number of plants be x and the ratio can be said as $\rm\;5x : 6x$

                                     $\begin{aligned}\rm 6x + \dfrac{5x}{2} &= 850\\\\\dfrac{6x(2)+5x}{2} &=850\\\dfrac{12x+5x}{2} &=850\\17x&=850(2)\\17x&=1700\\x&=\dfrac{1700}{100} \\x&=100\end$

Therefore by multiplying the value of x to the ratio plants in Ralph's garden we got,

                      $\begin{aligned}\rm\: plants\:in\:Ralph's\:garden&= 6x\\\rm plants\:in\:Ralph's\:garden&= 6\: \times 100\\\rm\:plants\:in\:Ralph's\:garden&=600\end$

Hence the number of plants Ralph's garden had in the first place is 600.

Learn more about Ratio here:

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