With the given information, we can create several equations:
120 = 12x + 2y
150 = 10x + 10y
With x being the number of rose bushes, and y being the number of gardenias.
To find the values of the variables, we can use two methods: Substitution or Elimination
For this case, let us use elimination. To begin, let's be clear that we are going to be adding these equations together. Therefore, in order to get the value of one variable, we must cancel one of them out - it could be x or y, it doesn't matter which one you decide to cancel out. Let's cancel the x out:
We first need to multiply the equations by numbers that would cause the x's to cancel out - and this can be done as follows:
-10(120 = 12x + 2y)
12(150 = 10x + 10y) => Notice how one of these is negative
Multiply out:
-1200 = -120x - 20y
+ 1800 = 120x + 120y => Add these two equations together
---------------------------------
600 = 100y
Now we can solve for y:
y = 6
With this value of y known, we can then pick an equation from the beginning of the question, and plug y in to solve for x:
120 = 12x + 2y => 120 = 12x + 2(6)
Now we can solve for x:
120 = 12x + 12 => 108 = 12x
x = 9
So now we know that x = 9, and y = 6.
With rose bushes being x, we now know that the cost of 1 rose bush is $9.
With gardenias being y, we now know that the cost of 1 gardenia is $6.
<span>0.5x - 0.1 = -2.9
When you multiply each side of an equation by the same number,
you don't change the equation or its solution. If you want to get rid
of the decimals, you could multiply each side by 10. Then the
equation is
5x - 1 = -29
You should be able to solve that without help.
But I'm about to take your points, so here's
how to solve that equation:
</span><span><span>5x - 1 = -29
Add 1 to each side: 5x = -28
Divide each side by 5 : x = -28 / 5
Simplify the solution: x = -5 and 4/5 .
Again ... this is the same solution as the original equation
if we hadn't gotten rid of the decimals.
</span></span>
120 ways. More details in attachment.
