Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
For each question, write an algebraic equation and solve it. Write your answer in simplest form.
Elizabeth has
1
7
10
as many plants as Rosalie has in her garden. If Elizabeth has 51 plants, how many plants does Rosalie have in her garden
Let x = the number of plants Rosalie has in her garden.
7x + 10x = 51
17x = 51
x = 3
Rosalie has 3 plants in her garden.
Let's call the number of plants that Rosalie has in her garden R.
We're given that Elizabeth has 1/7 of the number of plants that Rosalie has. Therefore, we can write the equation:
1/7R = 51
To solve for R, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 7:
(1/7R) * 7 = 51 * 7
R = 357
Therefore, Rosalie has 357 plants in her garden.
Let's call the number of plants Rosalie has in her garden as "R".
Given that Elizabeth has 17/10 times as many plants as Rosalie, we can write the equation:
Elizabeth's plants = (17/10) * Rosalie's plants
Substituting the given values:
51 = (17/10) * R
To solve for R, we can multiply both sides of the equation by 10/17 to isolate R:
(10/17) * 51 = R
Doing the calculation on the left side, we get:
10 * 51 / 17 = R
Therefore, Rosalie has R = 30 plants in her garden.
To solve this problem, we need to set up an algebraic equation.
Let's denote the number of plants Rosalie has as "x".
According to the problem, Elizabeth has 17/10 times as many plants as Rosalie. So we can write the equation as:
Elizabeth's Plants = 17/10 * Rosalie's Plants
Given that Elizabeth has 51 plants, we can substitute this value into the equation:
51 = 17/10 * x
To solve for x, we need to isolate it on one side of the equation. To do this, we can multiply both sides of the equation by the reciprocal of 17/10, which is 10/17:
51 * (10/17) = (17/10 * x) * (10/17)
Simplifying the equation:
510/17 = x
Now we can divide the numerator by the denominator to get the value of x:
x = 510/17
To express the answer in simplest form, we can divide the numerator and denominator by their greatest common divisor, which in this case is 17:
x = 30
Therefore, Rosalie has 30 plants in her garden.