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?
Jim bought 4 petunias.
Jim bought 15 petunias.
Jim bought 15 begonias.
Jim bought 18 begonias.
To solve this problem, we can set up a system of equations.
Let's assume Jim bought x petunias and y begonias.
From the problem, we know that:
Petunias cost $11 per pot, so the number of petunias multiplied by the cost per pot should equal the total cost of petunias: 11x.
Begonias cost $15 per pot, so the number of begonias multiplied by the cost per pot should equal the total cost of begonias: 15y.
Jim bought a total of 19 potted plants, so the number of petunias and begonias should add up to 19: x + y = 19.
Jim spent a total of $225 on the plants, so the total cost of petunias plus the total cost of begonias should equal $225: 11x + 15y = 225.
We now have a system of equations:
x + y = 19
11x + 15y = 225
To solve this system, we can use substitution or elimination method.
Using the substitution method:
From the first equation (x + y = 19), we can solve for x: x = 19 - y.
Substituting this into the second equation: 11(19 - y) + 15y = 225.
Expanding and simplifying: 209 - 11y + 15y = 225.
Combining like terms: 4y = 16.
Dividing both sides by 4: y = 4.
Since y represents the number of begonias, Jim bought 4 begonias.
To find the number of petunias (x), we can substitute this value back into the first equation:
x + 4 = 19.
Subtracting 4 from both sides: x = 15.
Therefore, the correct statement is:
Jim bought 15 petunias.