Jim bought some potted plants: %0D%0A%0D%0APetunias cost $11 per pot and Begonias cost $15 per pot.%0D%0A%0D%0AJim bought 19 potted plants in all and spent a total of $225 on the plants.%0D%0A%0D%0AWhich would be a correct statement?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AJim bought 18 begonias.%0D%0AJim bought 18 begonias.%0D%0A%0D%0AJim bought 15 petunias.%0D%0AJim bought 15 petunias.%0D%0A%0D%0AJim bought 4 petunias.%0D%0AJim bought 4 petunias.%0D%0A%0D%0AJim bought 15 begonias.
Jim bought 15 petunias.
To determine which statement is correct, we can calculate the number of each type of potted plant that Jim bought.
Let's assign a variable to represent the number of petunias and begonias Jim bought. Let's say P represents the number of petunias and B represents the number of begonias.
We can set up a system of equations to represent the given information:
P + B = 19 (Jim bought 19 potted plants in total)
11P + 15B = 225 (Jim spent a total of $225)
To solve this system of equations, we can use substitution or elimination. For simplicity, let's use substitution.
From the first equation, we can express P in terms of B by subtracting B from both sides:
P = 19 - B
Substituting this expression for P in the second equation, we have:
11(19 - B) + 15B = 225
Expanding and simplifying, we get:
209 - 11B + 15B = 225
Combine like terms:
4B = 16
Divide both sides by 4:
B = 4
Now that we know B = 4, we can substitute this value back into the expression we found for P to find the number of petunias:
P = 19 - B = 19 - 4 = 15
Therefore, Jim bought 15 petunias (option: Jim bought 15 petunias) and 4 begonias.
To find out the correct statement, we need to solve the given problem step-by-step.
Let's assume Jim bought x petunias and y begonias.
According to the given information:
Petunias cost $11 per pot, so the cost of petunias = 11x.
Begonias cost $15 per pot, so the cost of begonias = 15y.
Jim bought 19 potted plants in all, so we have the equation x + y = 19. (Equation 1)
Jim spent a total of $225 on the plants, so we have the equation 11x + 15y = 225. (Equation 2)
Let's solve these equations simultaneously.
To eliminate the variables, let's multiply Equation 1 by 11, and Equation 2 by -1:
11(x + y) = 11(19) --> 11x + 11y = 209. (Equation 3)
-1(11x + 15y) = -1(225) --> -11x - 15y = -225. (Equation 4)
Now, we add Equation 3 and Equation 4 together:
(11x + 11y) + (-11x - 15y) = 209 + (-225)
11x - 11x + 11y - 15y = -16
-4y = -16
y = -16/-4
y = 4
Substitute the value of y in Equation 1:
x + 4 = 19
x = 19 - 4
x = 15
So, Jim bought x = 15 petunias and y = 4 begonias.
The correct statement is: Jim bought 15 petunias.