Answer:
One rose costs $5.96, and one daisy costs $7.00
Explanation:
Let's start with part 1 of the word problem. The question asks us to set up a system of equations, where r represents the cost of a rose, and d represents the cost of a daisy.
Setting up our System of Equations
We know that she bought three roses and two daisies for $31.88, meaning...
3r + 2d = 3188 (represent the costs of the flowers in cents not dollars)
We also know that she went back and bought two roses and one daisy for $18.92, which gives us our second equation:
2r + d = 1892
Now, we have our system of equations:
3r + 2d = 3188
2r + d = 1892
Solving the System of Equations
There are many ways to solve a system of equations. For this question, we will be using the substitution method.
Start by writing the second equation in terms of d:
d = 1892 - 2r
Then, substitute this value of d into the first equation:
3r + 2(1892 - 2r) = 3188
Distribute the 2:
3r + 2 × 1892 - 2 × 2r = 3188
3r + 3784 - 4r = 3188
Combine like terms:
-1r + 3784 = 3188
Subtract 3784 from both sides:
-1r + 3784 - 3784 = 3188 - 3784
-1r = -596
Finally, divide both sides by -1:
r = 596
Plugging in this value back into our second equation, we get:
d = 1892 - 2(596) = 700
Now, let's change the values from cents to dollars...
One rose costs $5.96 and one daisy costs $7.00