Michelle bought some potted plants.
Petunias cost $7 per pot.
Begonias cost $8 per pot.
She bought 22 potted plants and spent a total of $163. How many petunias did she buy?
Let's use a system of equations to solve the problem:
P = number of petunias
B = number of begonias
P + B = 22 (she bought a total of 22 potted plants)
7P + 8B = 163 (she spent a total of $163)
We can use the first equation to solve for one of the variables in terms of the other:
B = 22 - P
We can substitute this into the second equation and simplify:
7P + 8(22 - P) = 163
7P + 176 - 8P = 163
-P = -13
P = 13
Therefore, Michelle bought 13 petunias. We can check our answer by finding the number of begonias:
B = 22 - P = 22 - 13 = 9
She bought 13 petunias and 9 begonias, which adds up to a total of 22 potted plants. We can also check the total cost:
7P + 8B = 7(13) + 8(9) = 91 + 72 = 163
The total cost is indeed $163.
Let's assume Michelle bought x petunias and y begonias.
According to the given information, the cost of each petunia is $7, and the cost of each begonia is $8.
So, the equation for the total number of plants is x + y = 22 (since she bought a total of 22 plants).
The equation for the total cost is 7x + 8y = 163 (since she spent a total of $163).
We can solve these equations simultaneously to find the values of x and y.
Multiply the first equation by 7:
7x + 7y = 154
Now subtract this equation from the second equation:
7x + 8y - (7x + 7y) = 163 - 154
y = 9
Substitute the value of y in the first equation:
x + 9 = 22
x = 22 - 9
x = 13
Therefore, Michelle bought 13 petunias.
To find out how many petunias Michelle bought, we can set up a system of equations based on the given information.
Let's assume that Michelle bought x petunias and y begonias.
According to the first piece of information, petunias cost $7 per pot. So the total cost of the petunias would be 7x.
Similarly, begonias cost $8 per pot. So the total cost of the begonias would be 8y.
According to the second piece of information, Michelle bought 22 potted plants in total. So we can write the equation:
x + y = 22 (equation 1)
According to the third piece of information, she spent a total of $163. So we can write the equation:
7x + 8y = 163 (equation 2)
Now we can solve this system of equations to find the values of x and y.
One way to solve the system is to multiply the equation 1 by 7 and subtract it from equation 2. This will eliminate the x variable:
7x + 8y - 7x - 7y = 163 - 7 * 22
y = 163 - 7 * 22
y = 163 - 154
y = 9
Now, substitute the value of y back into equation 1 to find the value of x:
x + 9 = 22
x = 22 - 9
x = 13
Therefore, Michelle bought 13 petunias.