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)
A. Jim bought 15 begonias.
B. Jim bought 15 petunias.
C. Jim bought 4 petunias.
D. Jim bought 18 begonias.
Let's assume Jim bought x petunias and y begonias.
From the given information, we can form two equations:
x + y = 19 (since Jim bought 19 potted plants in total)
11x + 15y = 225 (since Jim spent a total of $225 on the plants)
To solve this system of equations, we can use the method of substitution.
From the first equation, we can isolate x by subtracting y from both sides:
x = 19 - y
Substituting x in the second equation:
11(19 - y) + 15y = 225
209 - 11y + 15y = 225
4y = 16
y = 4
Substituting y = 4 back into the first equation:
x + 4 = 19
x = 15
Therefore, Jim bought 15 petunias and 4 begonias.
The correct statement is:
B. Jim bought 15 petunias.
To solve this problem, let's assume that Jim bought x number of Petunias and y number of Begonias.
Given that Petunias cost $11 per pot and Begonias cost $15 per pot, we can set up the following equations:
x + y = 19 (equation 1) --- (since Jim bought a total of 19 potted plants)
11x + 15y = 225 (equation 2) --- (since Jim spent a total of $225 on the plants)
To find the correct statement, we need to determine the values of x and y that satisfy both equations 1 and 2.
Let's solve the system of equations:
From equation 1, we can express x in terms of y:
x = 19 - y
Substitute this value of x into equation 2:
11(19 - y) + 15y = 225
Simplify the equation:
209 - 11y + 15y = 225
-4y = 16
y = 16 / -4
y = -4
Substitute the value of y into equation 1 to find x:
x + (-4) = 19
x - 4 = 19
x = 19 + 4
x = 23
Since the value of y is negative (-4), it doesn't make sense to have a negative number of Begonias. Therefore, the correct statement would be:
C. Jim bought 4 petunias.
To find the correct statement, we need to solve the given problem using the information provided.
Let's assign variables to represent the number of Petunias and Begonias Jim bought.
Let x be the number of Petunias.
Let y be the number of Begonias.
From the information given:
1) Petunias cost $11 per pot, so the cost of x Petunias would be 11x dollars.
2) Begonias cost $15 per pot, so the cost of y Begonias would be 15y dollars.
3) Jim bought 19 potted plants in total, so the equation x + y = 19 holds.
4) Jim spent a total of $225 on the plants, so the equation 11x + 15y = 225 holds.
Now, we have a system of two equations:
x + y = 19
11x + 15y = 225
To find the correct statement, let's solve this system.
One way to solve the system is through substitution:
1) Solve the first equation for x: x = 19 - y.
2) Substitute this value of x into the second equation: 11(19 - y) + 15y = 225.
3) Simplify: 209 - 11y + 15y = 225.
4) Combine like terms: 4y = 16.
5) Solve for y: y = 4.
Now, substitute this value of y back into the first equation to find x:
x + 4 = 19
x = 15.
From this calculation, we can conclude that Jim bought 15 Petunias and 4 Begonias.
Therefore, the correct statement is C. Jim bought 4 petunias.