Karen 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 Karen buy?
Responses
7
7
11
11
9
9 petunias
Why did the plants go on strike? Because they were sick of being "potted" all day!
Let's represent the number of petunias as x and the number of begonias as y.
We know that the cost of one petunia is $7 and the cost of one begonia is $8.
So, the total cost of petunias is 7x and the total cost of begonias is 8y.
We also know that Karen bought a total of 22 potted plants, so the equation for the total number of plants is x + y = 22.
We are given that the total spent was $163, so the equation for the total cost is 7x + 8y = 163.
Now, we can solve these equations to find the values of x and y.
From the equation x + y = 22, we can express y in terms of x:
y = 22 - x
Substituting this into the total cost equation, we get:
7x + 8(22 - x) = 163
Simplifying the equation, we have:
7x + 176 - 8x = 163
-1x = -13
Dividing both sides by -1, we find:
x = 13
So, Karen bought 13 petunias.
To figure out how many petunias Karen bought, we can set up a system of equations based on the given information.
Let's assume that Karen bought x petunias and y begonias.
From the information given, we know that Karen bought a total of 22 potted plants. So we can write the first equation as:
x + y = 22 (equation 1)
We also know that each petunia costs $7 and each begonia costs $8. The total amount Karen spent was $163. So we can write the second equation as:
7x + 8y = 163 (equation 2)
To solve this system of equations, we can use the method of substitution.
From equation 1, we can solve for x:
x = 22 - y
Now substitute this value of x in equation 2:
7(22 - y) + 8y = 163
Expand and simplify:
154 - 7y + 8y = 163
Combine like terms:
y = 9
Now substitute the value of y back into equation 1 to find x:
x + 9 = 22
x = 22 - 9
x = 13
Therefore, Karen bought 13 petunias.