Jim bought some potted plants:
Petunias cost $11 per pot and Begonias cost $15 per pot.
Jim bought 19 potted plants in all and spent a total of $225 on the plants.
Which would be a correct statement?
(1 point)
Responses
Jim bought 4 petunias.
Jim bought 4 petunias.
Jim bought 15 petunias.
Jim bought 15 petunias.
Jim bought 18 begonias.
Jim bought 18 begonias.
Jim bought 15 begonias.
The correct statement would be:
Jim bought 15 begonias.
To solve this problem, we can set up a system of equations based on the given information. Let's define:
P = number of petunias bought by Jim
B = number of begonias bought by Jim
We know that Jim bought a total of 19 potted plants, so our first equation is:
P + B = 19 Equation 1
We also know that the cost of each petunia is $11 and the cost of each begonia is $15. Since Jim spent a total of $225 on the plants, our second equation is:
11P + 15B = 225 Equation 2
Now we can solve this system of equations. One way to do this is to multiply Equation 1 by 11 to get rid of P:
11P + 11B = 209 Equation 3
Now we can subtract Equation 3 from Equation 2 to eliminate P:
11P + 15B - (11P + 11B) = 225 - 209
15B - 11B = 16
4B = 16
B = 4
So Jim bought 4 begonias. Now we can substitute this value of B back into Equation 1 to solve for P:
P + 4 = 19
P = 15
Therefore, a correct statement would be: Jim bought 15 petunias.
To find the correct statement, let's assume Jim bought "x" petunias and "y" begonias.
According to the given information, the total number of potted plants bought by Jim is 19. So, we can write the equation:
x + y = 19 ---(Equation 1)
The cost of each petunia is $11, and the cost of each begonia is $15. The total amount spent on the plants is $225. So, we can write the equation:
11x + 15y = 225 ---(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
From Equation 1, we can solve for "x":
x = 19 - y
Substituting this value of "x" into Equation 2:
11(19 - y) + 15y = 225
209 - 11y + 15y = 225
Combine like terms:
4y = 16
Divide both sides by 4:
y = 4
Substituting this value of "y" back into Equation 1:
x + 4 = 19
Subtracting 4 from both sides:
x = 15
Therefore, the correct statement is:
Jim bought 15 petunias and 4 begonias.
So, the correct option is:
Jim bought 15 petunias.